Liverpool hold a precious advantage going into the Capital One Cup semi-final second leg after Jordon Ibe's goal gave them victory at Stoke City.
Jurgen Klopp's side take the lead to Anfield for the return on 26 January despite losing influential midfield man Philippe Coutinho and defender Dejan Lovren to hamstring injuries before half-time.
Ibe, on for Coutinho, struck at the far post in the 37th minute after clever build-up work by Adam Lallana and Joe Allen.
Stoke failed to reproduce the form that has brought them home wins against Chelsea, Manchester City and Manchester United in recent times and, when they did force an opening, Liverpool keeper Simon Mignolet saved well from Glen Johnson and Joselu.
Substitute Jon Walters wasted their best chance deep into stoppage time and Liverpool are now favourites to meet either Everton or Manchester City at Wembley.
Relive Liverpool's win
Klopp left the media to guess at the "three words" he delivered to his players after a dismal performance in defeat at West Ham United on Saturday.
He had no need to rein in his message here as Liverpool bristled with an intensity from the first whistle that shocked Stoke City in such a manner they struggled to recover any rhythm or composure.
It was another example of the two-faced nature of Liverpool's performances under Klopp since he arrived to succeed the sacked Brendan Rodgers in early October.
This display, full of steely resolve and the incessant pressing Klopp demands, was more akin to the outstanding away victories at Chelsea (3-1), Manchester City (4-1) and the 6-1 win at Southampton in the quarter-final.
And yet Klopp has still had to suffer the frustration of Liverpool barely turning up in losses at Newcastle United, Watford and West Ham.
This was more like the model of what he will expect on a consistent basis when he has really settled into his work at Liverpool - and it has given him a big opportunity of marking his first season with a Wembley appearance.
This was a huge night at the Britannia Stadium as Stoke's players attempt to write their names alongside those who famously won the League Cup for the Potters against Chelsea at Wembley in 1972.
And anticipation had been elevated by the impressive form shown by Mark Hughes' side, a potent blend of silk and steel that arguably had them as favourites before the game.
It was to be a disappointing 90 minutes for the hosts as Liverpool appeared to stun them from kick-off by pressurising them into mistakes, and they simply never recovered enough to build up a head of steam.
Mignolet made a couple of important stops and Stoke felt they had penalty claims when Alberto Moreno tangled with Glenn Whelan, but Liverpool closed down their big players such as Bojan, Xherdan Shaqiri and Marko Arnautovic to deserve their victory.
No-one should dismiss Stoke's chances as they have shown so much quality already this season - but they have left themselves a huge task in the return.
After young Belgian striker Divock Origi went lame in the Boxing Day victory against Leicester City at Anfield, Klopp pointed out in colourful terms that "hamstring" was his least favourite word of 2015.
It is not shaping up any better in 2016 as Coutinho and Lovren both limped off clutching their hamstrings before half-time - adding to Liverpool's already lengthy injury list. They may be joined by Kolo Toure, who ended the game clutching the back of his right leg.
Klopp's "gegenpressing" style, intense and physical as opponents are put under pressure, is demanding and requires high levels of fitness - and maybe it is taking some getting used to for his new charges.
And there is no doubt Liverpool are also suffering a run of bad luck that is filling up the treatment room at their Melwood training headquarters.
Martin Skrtel, as well as Origi, is nursing a hamstring problem while James Milner has only just returned from a similar injury.
Joe Gomez and Danny Ings suffered long-term knee ligament problems before Klopp's arrival while Jordan Henderson's heel problem is a recurrence of a problem he had earlier in the season.
Jordan Rossiter was sidelined by a hamstring problem after initially suffering the injury with England's youngsters while Daniel Sturridge's many problems have already occupied much of Klopp's early time at Anfield.
The German is waiting for the day when he will have all his Liverpool players fit - but that day looks as far away as ever.
Stoke City manager Mark Hughes said: "People might want to criticise what we did in the first half but sometimes you have to credit the opposition.
"They restricted what we wanted to do in terms of getting people around the ball and restricting space and they did that to good effect and we had to improve in the second half.
"The key from our point of view is that we didn't concede again and the danger was that if we over committed and conceded another one that would have been a huge task to go to Anfield and claw it back."
Liverpool boss Jurgen Klopp told BSports Radio 5 live: "The only thing we can criticise is our finishing again. We had a good structure, played football good, everything was good but we don't make enough goals.
"The biggest problem for us is we have two and maybe three injured players again."
Liverpool travel to League Two Exeter City in the FA Cup on Friday night, before Arsenal and then Manchester United visit Anfield in the Premier League. Stoke travel to League One Doncaster in the FA Cup on Saturday, before entertaining Norwich and Arsenal in the league.
Full Time Match ends, Stoke City 0, Liverpool 1.
90:00 +3:38 Full timeFull Time Second Half ends, Stoke City 0, Liverpool 1.
90:00 +3:11Attempt missed. Jonathan Walters (Stoke City) left footed shot from the left side of the box misses to the right. Assisted by Peter Crouch with a headed pass.
90:00 +1:48Attempt missed. Jonathan Walters (Stoke City) header from the centre of the box is close, but misses to the left. Assisted by Joselu with a cross.
87:08Offside, Stoke City. Glen Johnson tries a through ball, but Marko Arnautovic is caught offside.
87:07Attempt missed. Glen Johnson (Stoke City) left footed shot from outside the box misses to the right following a corner.
86:31Corner, Stoke City. Conceded by Simon Mignolet.
85:14Foul by Philipp Wollscheid (Stoke City).
85:14Christian Benteke (Liverpool) wins a free kick in the attacking half.
82:49 SubstitutionSubstitution Substitution, Stoke City. Peter Crouch replaces Xherdan Shaqiri.
81:49Corner, Stoke City. Conceded by Kolo Touré.
80:30Erik Pieters (Stoke City) wins a free kick on the left wing.
80:30Foul by Adam Lallana (Liverpool).
79:04Foul by Erik Pieters (Stoke City).
79:04Adam Lallana (Liverpool) wins a free kick in the defensive half.
78:12 SubstitutionSubstitution Substitution, Liverpool. Christian Benteke replaces Joe Allen.
77:43Attempt missed. Roberto Firmino (Liverpool) right footed shot from outside the box is too high. Assisted by Alberto Moreno.
76:59Foul by Ryan Shawcross (Stoke City).
76:59Roberto Firmino (Liverpool) wins a free kick on the left wing.
76:25Attempt missed. Joselu (Stoke City) left footed shot from the left side of the six yard box misses to the left. Assisted by Xherdan Shaqiri with a cross following a corner.
Corner, Stoke City. Conceded by Simon Mignolet.
75:56Attempt saved. Joselu (Stoke City) right footed shot from outside the box is saved in the top right corner. Assisted by Glenn Whelan.
72:22 BookingBooking Simon Mignolet (Liverpool) is shown the yellow card.
71:34Erik Pieters (Stoke City) wins a free kick on the left wing.
71:34Foul by Adam Lallana (Liverpool).
71:15Philipp Wollscheid (Stoke City) wins a free kick in the defensive half.
71:15Foul by Roberto Firmino (Liverpool).
68:58 SubstitutionSubstitution Substitution, Stoke City. Joselu replaces Bojan.
68:19Attempt missed. Ryan Shawcross (Stoke City) header from the centre of the box is too high. Assisted by Jonathan Walters with a cross.
67:17Attempt missed. Jordon Ibe (Liverpool) right footed shot from the left side of the box is close, but misses to the left. Assisted by Roberto Firmino.
64:35Attempt missed. James Milner (Liverpool) left footed shot from the left side of the box misses to the right following a set piece situation.
63:50Foul by Glen Johnson (Stoke City).
63:50Jordon Ibe (Liverpool) wins a free kick on the left wing.
62:44Attempt missed. Roberto Firmino (Liverpool) left footed shot from outside the box is close, but misses to the right. Assisted by Emre Can.
59:32Corner, Stoke City. Conceded by Kolo Touré.
59:21Ibrahim Afellay (Stoke City) wins a free kick in the defensive half.
59:21Foul by James Milner (Liverpool).
58:16Attempt missed. Roberto Firmino (Liverpool) right footed shot from the centre of the box is too high. Assisted by Adam Lallana.
52:01Attempt missed. Glen Johnson (Stoke City) right footed shot from the right side of the box is too high following a set piece situation.
51:59Attempt blocked. Ryan Shawcross (Stoke City) right footed shot from the centre of the box is blocked. Assisted by Glenn Whelan.
51:32Jonathan Walters (Stoke City) wins a free kick on the left wing.
51:32Foul by Kolo Touré (Liverpool).
48:17Offside, Liverpool. Joe Allen tries a through ball, but Adam Lallana is caught offside.
45:58Attempt missed. Emre Can (Liverpool) right footed shot from outside the box misses to the right. Assisted by Roberto Firmino.
45:00Second Half begins Stoke City 0, Liverpool 1.
45:00 SubstitutionSubstitution Substitution, Stoke City. Jonathan Walters replaces Geoff Cameron.
45:00 +3:18 Half timeHalf Time First Half ends, Stoke City 0, Liverpool 1.
45:00 +3:07Attempt saved. Glen Johnson (Stoke City) right footed shot from the centre of the box is saved in the centre of the goal.
45:00 +2:38Corner, Stoke City. Conceded by Alberto Moreno.
45:00 +2:36Attempt blocked. Xherdan Shaqiri (Stoke City) left footed shot from outside the box is blocked. Assisted by Bojan.
45:00 +1:53Glen Johnson (Stoke City) wins a free kick in the defensive half.
45:00 +1:53Foul by Roberto Firmino (Liverpool).
45:00 +0:41Attempt missed. Xherdan Shaqiri (Stoke City) left footed shot from outside the box is too high. Assisted by Ibrahim Afellay.
43:08Attempt blocked. Ibrahim Afellay (Stoke City) right footed shot from outside the box is blocked.
40:33Attempt missed. Jordon Ibe (Liverpool) right footed shot from the left side of the box misses to the right. Assisted by Adam Lallana with a cross.
38:40Corner, Liverpool. Conceded by Ryan Shawcross.
37:56Attempt missed. Marko Arnautovic (Stoke City) header from the centre of the box misses to the left. Assisted by Glen Johnson with a cross.
36:27 Goal scoredGoal! Goal! Stoke City 0, Liverpool 1. Jordon Ibe (Liverpool) left footed shot from the centre of the box to the bottom right corner. Assisted by Joe Allen.
36:26Attempt missed. Joe Allen (Liverpool) right footed shot from the centre of the box misses to the left. Assisted by Adam Lallana.
33:47 SubstitutionSubstitution Substitution, Liverpool. James Milner replaces Dejan Lovren because of an injury.
33:23Delay over. They are ready to continue.
31:43Delay in match Dejan Lovren (Liverpool) because of an injury.
27:37Attempt saved. Jordon Ibe (Liverpool) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Adam Lallana with a headed pass.
25:24Attempt missed. Glen Johnson (Stoke City) left footed shot from outside the box is too high following a corner.
24:47Corner, Stoke City. Conceded by Kolo Touré.
23:52Attempt missed. Jordon Ibe (Liverpool) right footed shot from outside the box is high and wide to the right. Assisted by Alberto Moreno.
23:28Attempt blocked. Roberto Firmino (Liverpool) left footed shot from the centre of the box is blocked. Assisted by Adam Lallana.
19:58Offside, Stoke City. Ibrahim Afellay tries a through ball, but Marko Arnautovic is caught offside.
17:57Delay over. They are ready to continue.
17:57 SubstitutionSubstitution Substitution, Liverpool. Jordon Ibe replaces Philippe Coutinho because of an injury.
16:55Delay in match Philippe Coutinho (Liverpool) because of an injury.
15:43Attempt blocked. Roberto Firmino (Liverpool) right footed shot from the centre of the box is blocked. Assisted by Dejan Lovren with a headed pass.
15:07Corner, Liverpool. Conceded by Ryan Shawcross.
15:06Attempt blocked. Roberto Firmino (Liverpool) right footed shot from the left side of the box is blocked.
14:44Attempt blocked. Ibrahim Afellay (Stoke City) right footed shot from outside the box is blocked. Assisted by Erik Pieters.
9:02Offside, Liverpool. Lucas Leiva tries a through ball, but Adam Lallana is caught offside.
7:16Attempt saved. Adam Lallana (Liverpool) right footed shot from outside the box is saved in the bottom right corner. Assisted by Roberto Firmino.
3:50Corner, Liverpool. Conceded by Philipp Wollscheid.
1:50Corner, Liverpool. Conceded by Glen Johnson.
1:14Corner, Liverpool. Conceded by Glenn Whelan.
0:34Attempt saved. Roberto Firmino (Liverpool) right footed shot from outside the box is saved in the bottom right corner.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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