Jurgen Klopp picked up his first league win at Anfield as James Milner's second-half penalty gave Liverpool the points in a stale game against Swansea.
Milner converted after Swans full-back Neil Taylor was penalised for handball.
Liverpool - so impressive in their win at Manchester City last week - were flat for large periods but did see captain Jordan Henderson return from injury as a substitute.
Swansea have now won once in 10 league games since August.
Garry Monk's side failed to record a single effort on target in 90 minutes and face the top two in Leicester and Manchester City in their next two games.
Liverpool's last two Premier League games away from home have seen them record hugely impressive wins at champions Chelsea and leaders Manchester City, with Klopp's preferred 'gegenpressing' style well suited to winning the ball back quickly and hurting teams on the break.
But in three league games at home, the Reds have scored just three times under Klopp and remain a work in progress.
Despite a bright opening spell, during which Jordon Ibe forced defender Kyle Bartley to clear against his own post, the hosts soon ran out of steam and did not have an effort on target until the 52nd minute, when Ibe's tame shot was saved by Lukas Fabianski.
In truth, they were grateful to referee's assistant Simon Beck for the decisive moment when he awarded a penalty as Taylor blocked an Ibe cross with his arm.
Milner lifted the spot-kick high into the net to give Liverpool a sixth win in seven games in all competitions, which lifted them up to sixth in the table.
With former captain Steven Gerrard watching from the stands, perhaps the biggest plusses Liverpool fans can take from the win are the returns of Henderson and Daniel Sturridge.
Henderson - missing with a broken foot since the second game of the season in August - was handed the armband when he came on for the final 25 minutes, while Sturridge had a 19-minute run out for his first appearance since Klopp replaced Brendan Rodgers in October.
If Liverpool looked uninspiring in attack, Swansea's failure to test Simon Mignolet at all will give manager Monk plenty to ponder.
More worryingly it was the second time in the last three Premier League matches that Swansea failed to hit a single effort on target - also registering no attempts in the 1-0 defeat at Norwich.
Monk - who took charge in February 2014 - guided Swansea to their highest Premier League finish of eighth last season.
When they beat Manchester United at the end of August the Swans were in fourth but they have won only once since, scoring seven goals in 10 matches.
Monk can point to a harsh handball decision which settled the game but, in attack, his side offered precious little threat.
Centre-forward Eder was often isolated and replacement Bafetimbi Gomis has lost the spark which saw him score in each of the opening four games of the season.
With testing games against Leicester and Manchester City to come a four-point gap to the relegation zone is a real concern.
Liverpool manager Jurgen Klopp told BSports: "It was really difficult for both teams, the wind was in the stadium more than the stands.
"Swansea defended very well. They had some problems in the last few games but they were more compact. I am proud of the lads. It is a good result in difficult circumstances."
Liverpool face a trip to Southampton on Wednesday for a League Cup quarter-final, before facing Newcastle at St James' Park next Sunday.
Life does not get easier for Swansea as they host Jamie Vardy's Leicester next Saturday, and then travel to leaders Manchester City the week after.
Full Time Match ends, Liverpool 1, Swansea City 0.
90:00 +5:29 Full timeFull Time Second Half ends, Liverpool 1, Swansea City 0.
90:00 +5:01Corner, Swansea City. Conceded by Kolo Touré.
90:00 +4:40Foul by James Milner (Liverpool).
90:00 +4:40Kyle Naughton (Swansea City) wins a free kick in the defensive half.
90:00 +4:01 SubstitutionSubstitution Substitution, Liverpool. Kolo Touré replaces Jordon Ibe.
90:00 +2:56 BookingBooking Simon Mignolet (Liverpool) is shown the yellow card.
90:00 +1:51Corner, Swansea City. Conceded by Emre Can.
90:00 +1:50Attempt blocked. Bafétimbi Gomis (Swansea City) right footed shot from outside the box is blocked. Assisted by Ashley Williams.
89:20Corner, Liverpool. Conceded by Kyle Bartley.
86:23Jordon Ibe (Liverpool) wins a free kick in the attacking half.
86:23Foul by Neil Taylor (Swansea City).
81:35Corner, Swansea City. Conceded by Nathaniel Clyne.
81:15Delay over. They are ready to continue.
80:31Delay in match Kyle Bartley (Swansea City) because of an injury.
79:52Attempt missed. Ashley Williams (Swansea City) header from the centre of the box misses to the right following a corner.
79:49Attempt blocked. Jack Cork (Swansea City) right footed shot from outside the box is blocked.
79:21Corner, Swansea City. Conceded by Martin Skrtel.
78:22Corner, Swansea City. Conceded by Nathaniel Clyne.
78:02Attempt blocked. Bafétimbi Gomis (Swansea City) right footed shot from the right side of the box is blocked. Assisted by André Ayew.
Corner, Swansea City. Conceded by Nathaniel Clyne.
76:30Attempt blocked. Jefferson Montero (Swansea City) right footed shot from outside the box is blocked. Assisted by Bafétimbi Gomis.
75:21Foul by Alberto Moreno (Liverpool).
75:21André Ayew (Swansea City) wins a free kick in the defensive half.
74:01Attempt missed. James Milner (Liverpool) left footed shot from the left side of the box misses to the right. Assisted by Jordan Henderson.
71:49 SubstitutionSubstitution Substitution, Swansea City. Jefferson Montero replaces Wayne Routledge.
70:17 SubstitutionSubstitution Substitution, Liverpool. Daniel Sturridge replaces Christian Benteke.
69:38 BookingBooking Kyle Bartley (Swansea City) is shown the yellow card for a bad foul.
69:32James Milner (Liverpool) wins a free kick on the left wing.
69:32Foul by Kyle Bartley (Swansea City).
68:19 SubstitutionSubstitution Substitution, Swansea City. Bafétimbi Gomis replaces Eder because of an injury.
65:41Delay over. They are ready to continue.
64:54Delay in match Eder (Swansea City) because of an injury.
64:31 BookingBooking Martin Skrtel (Liverpool) is shown the yellow card for a bad foul.
64:28Foul by Martin Skrtel (Liverpool).
64:28Eder (Swansea City) wins a free kick on the left wing.
64:11 SubstitutionSubstitution Substitution, Swansea City. Jack Cork replaces Leon Britton.
63:56 SubstitutionSubstitution Substitution, Liverpool. Jordan Henderson replaces Roberto Firmino.
61:58 Goal scoredGoal! Goal! Liverpool 1, Swansea City 0. James Milner (Liverpool) converts the penalty with a right footed shot to the high centre of the goal.
60:59Penalty conceded by Neil Taylor (Swansea City) with a hand ball in the penalty area.
60:54Attempt blocked. Roberto Firmino (Liverpool) left footed shot from the centre of the box is blocked. Assisted by Nathaniel Clyne.
59:36Foul by Alberto Moreno (Liverpool).
59:36Kyle Naughton (Swansea City) wins a free kick in the defensive half.
59:20Adam Lallana (Liverpool) wins a free kick on the left wing.
59:20Foul by Kyle Naughton (Swansea City).
56:44Attempt blocked. Roberto Firmino (Liverpool) header from the centre of the box is blocked. Assisted by Alberto Moreno with a cross.
56:15Corner, Liverpool. Conceded by Leon Britton.
56:14Attempt blocked. Christian Benteke (Liverpool) left footed shot from the left side of the box is blocked.
54:02Foul by Jordon Ibe (Liverpool).
54:02André Ayew (Swansea City) wins a free kick in the defensive half.
53:19Delay over. They are ready to continue.
52:33Delay in match Eder (Swansea City) because of an injury.
52:02Attempt missed. Dejan Lovren (Liverpool) header from the centre of the box is too high. Assisted by Adam Lallana with a cross following a corner.
51:20Corner, Liverpool. Conceded by Lukasz Fabianski.
51:18Attempt saved. Jordon Ibe (Liverpool) right footed shot from outside the box is saved in the bottom left corner. Assisted by Alberto Moreno.
50:06Corner, Liverpool. Conceded by Ashley Williams.
49:06Attempt missed. Ki Sung-yueng (Swansea City) left footed shot from outside the box is just a bit too high. Assisted by Gylfi Sigurdsson.
45:00Second Half begins Liverpool 0, Swansea City 0.
45:00 +1:07 Half timeHalf Time First Half ends, Liverpool 0, Swansea City 0.
45:00 +0:42Attempt missed. Eder (Swansea City) right footed shot from outside the box misses to the left. Assisted by Leon Britton.
44:21Corner, Liverpool. Conceded by Kyle Bartley.
41:55Attempt missed. Alberto Moreno (Liverpool) left footed shot from outside the box is too high from a direct free kick.
40:47Christian Benteke (Liverpool) wins a free kick in the attacking half.
40:47Foul by Kyle Bartley (Swansea City).
37:40Delay over. They are ready to continue.
36:54Delay in match Kyle Bartley (Swansea City) because of an injury.
36:45Foul by Christian Benteke (Liverpool).
36:45Kyle Bartley (Swansea City) wins a free kick in the attacking half.
26:36Corner, Swansea City. Conceded by Dejan Lovren.
24:55 BookingBooking James Milner (Liverpool) is shown the yellow card for a bad foul.
24:48Foul by James Milner (Liverpool).
24:48André Ayew (Swansea City) wins a free kick on the left wing.
24:16Corner, Liverpool. Conceded by Ashley Williams.
24:10Attempt blocked. Jordon Ibe (Liverpool) right footed shot from the right side of the box is blocked. Assisted by Alberto Moreno with a cross.
23:09Corner, Liverpool. Conceded by Ashley Williams.
21:40Corner, Liverpool. Conceded by Gylfi Sigurdsson.
20:45Attempt blocked. Adam Lallana (Liverpool) left footed shot from the centre of the box is blocked. Assisted by Nathaniel Clyne.
19:04Emre Can (Liverpool) wins a free kick on the left wing.
19:04Foul by Eder (Swansea City).
18:02Foul by Martin Skrtel (Liverpool).
18:02Eder (Swansea City) wins a free kick in the defensive half.
8:06Foul by Christian Benteke (Liverpool).
8:06Kyle Naughton (Swansea City) wins a free kick in the defensive half.
7:22Attempt missed. Eder (Swansea City) header from the right side of the six yard box misses to the right. Assisted by Kyle Naughton with a cross.
6:41Foul by Christian Benteke (Liverpool).
6:41Ki Sung-yueng (Swansea City) wins a free kick in the attacking half.
6:28Foul by Emre Can (Liverpool).
6:28Gylfi Sigurdsson (Swansea City) wins a free kick in the attacking half.
6:08Foul by Dejan Lovren (Liverpool).
6:08Eder (Swansea City) wins a free kick in the defensive half.
3:50Offside, Swansea City. Kyle Bartley tries a through ball, but Eder is caught offside.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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