Blackburn will meet Oxford in the fourth round of the FA Cup after winning a feisty match at Newport.
Half-time substitute Jordan Rhodes headed home a superb winner for the Championship side, who had Chris Brown dismissed after 10 minutes for a scything tackle on Medy Elito.
Rovers had taken an early lead through a Ben Marshall penalty before Mark Byrne equalised from 25 yards.
League Two Newport had goalkeeper Joe Day sent off in injury time.
Day was dismissed for a professional foul on Rovers substitute Craig Conway, bringing down his opponent with a clumsy challenge just outside his area.
It was a frustrating end to a night that could have been very different for the Welsh side, especially given that Scott Boden wasted a wonderful chance to earn a replay, missing the target from six yards with a free header on 80 minutes.
This was arguably Newport's biggest FA Cup match since they lost 2-0 at Sunderland's Roker Park 30 years ago. And it was only the second game in charge for Warren Feeney, who took over following the departure of John Sheridan to Oldham last week - but it got off to a terrible start for the home side.
The original tie was postponed due to a waterlogged pitch but despite a tricky surface Marshall assuredly slotted home a penalty he won after being clipped by Scott Barrow with just eight minutes played.
Referee Charles Breakspear was back at the centre of the action just 90 seconds later, showing Brown a straight red card for his challenge on Elito.
With a man advantage, Newport soon found their rhythm against Paul Lambert's side and drew level before half-time via Byrne's thunderous strike, which went in off the underside of the bar.
Byrne had already gone close before scoring and Connor Dymond struck the woodwork for the home side.
However, Wales midfielder Tom Lawrence will have impressed his watching international manager Chris Coleman when his pinpoint cross was headed home by Rhodes in front of the away fans.
Newport manager Warren Feeney: "I am disappointed with the second-half performance but I can't be too hard on these players after that effort.
"The league is obviously our priority despite this being a big game for us. I'm proud of the performance of the players."
Blackburn, Paul Lambert: "We looked to be positive even a man down and in the second half only one side looked like winning it.
"We hope to have more good news for fans on Tuesday, with a new signing."
Full Time Match ends, Newport County 1, Blackburn Rovers 2.
90:00 +6:25 Full timeFull Time Second Half ends, Newport County 1, Blackburn Rovers 2.
90:00 +6:07Corner, Blackburn Rovers. Conceded by Joe Green.
90:00 +6:05Attempt saved. Ben Marshall (Blackburn Rovers) right footed shot from outside the box is saved in the bottom left corner.
90:00 +5:31 SubstitutionSubstitution Substitution, Newport County. Joe Green replaces Scott Barrow.
90:00 +4:11 DismissalDismissal Joe Day (Newport County) is shown the red card.
90:00 +4:08Foul by Joe Day (Newport County).
90:00 +4:08Craig Conway (Blackburn Rovers) wins a free kick in the attacking half.
89:30 SubstitutionSubstitution Substitution, Blackburn Rovers. Adam Henley replaces Corry Evans.
88:16Corner, Newport County. Conceded by Chris Taylor.
88:13Attempt blocked. Ben Davies (Newport County) header from a difficult angle on the left is blocked. Assisted by Scott Barrow.
87:36 BookingBooking Chris Taylor (Blackburn Rovers) is shown the yellow card for a bad foul.
87:33Aaron Collins (Newport County) wins a free kick in the attacking half.
87:33Foul by Chris Taylor (Blackburn Rovers).
84:57Attempt saved. Matt Taylor (Newport County) header from the centre of the box is saved in the centre of the goal. Assisted by Scott Barrow.
82:24Offside, Blackburn Rovers. Jordan Rhodes tries a through ball, but Craig Conway is caught offside.
82:03 SubstitutionSubstitution Substitution, Newport County. Matt Taylor replaces Connor Dymond.
80:52Attempt missed. Scott Boden (Newport County) header from very close range is close, but misses to the right. Assisted by Aaron Collins with a cross.
77:00Foul by Scott Barrow (Newport County).
77:00Chris Taylor (Blackburn Rovers) wins a free kick in the defensive half.
Substitution Substitution, Blackburn Rovers. Craig Conway replaces Tom Lawrence.
74:49 Goal scoredGoal! Goal! Newport County 1, Blackburn Rovers 2. Jordan Rhodes (Blackburn Rovers) header from the centre of the box to the centre of the goal. Assisted by Tom Lawrence with a cross.
72:59 BookingBooking Connor Dymond (Newport County) is shown the yellow card for a bad foul.
72:55Foul by Connor Dymond (Newport County).
72:55Thomas Spurr (Blackburn Rovers) wins a free kick on the left wing.
71:36Foul by Mark Byrne (Newport County).
71:36Corry Evans (Blackburn Rovers) wins a free kick in the attacking half.
69:46Ben Davies (Newport County) wins a free kick in the defensive half.
69:46Foul by Chris Taylor (Blackburn Rovers).
66:27Attempt missed. Scott Barrow (Newport County) right footed shot from outside the box is high and wide to the right. Assisted by Ben Davies.
66:04Connor Dymond (Newport County) wins a free kick in the attacking half.
66:04Foul by Corry Evans (Blackburn Rovers).
64:24Attempt missed. Jordan Rhodes (Blackburn Rovers) right footed shot from the centre of the box is high and wide to the right. Assisted by Corry Evans.
61:23Attempt missed. Chris Taylor (Blackburn Rovers) left footed shot from outside the box is high and wide to the left. Assisted by Jordan Rhodes.
60:25Foul by Aaron Collins (Newport County).
60:25Darragh Lenihan (Blackburn Rovers) wins a free kick in the defensive half.
58:16Attempt missed. Tom Lawrence (Blackburn Rovers) right footed shot from outside the box is high and wide to the right.
57:38Attempt missed. Mark Byrne (Newport County) right footed shot from outside the box misses to the right. Assisted by Scott Barrow.
57:05Attempt blocked. Corry Evans (Blackburn Rovers) right footed shot from outside the box is blocked.
56:31Corner, Blackburn Rovers. Conceded by Janoi Donacien.
56:30Attempt blocked. Chris Taylor (Blackburn Rovers) left footed shot from the centre of the box is blocked.
56:28Attempt blocked. Tom Lawrence (Blackburn Rovers) right footed shot from the centre of the box is blocked.
56:27Attempt blocked. Jordan Rhodes (Blackburn Rovers) right footed shot from the centre of the box is blocked. Assisted by Thomas Spurr with a cross.
54:36Corner, Blackburn Rovers. Conceded by Janoi Donacien.
51:07Delay over. They are ready to continue.
50:13Delay in match Janoi Donacien (Newport County) because of an injury.
50:13Delay in match Darragh Lenihan (Blackburn Rovers) because of an injury.
50:00Attempt blocked. Connor Dymond (Newport County) right footed shot from the centre of the box is blocked. Assisted by Scott Boden.
49:09Corner, Newport County. Conceded by Corry Evans.
47:50Foul by Danny Holmes (Newport County).
47:50Thomas Spurr (Blackburn Rovers) wins a free kick on the left wing.
46:49Foul by Tom Owen-Evans (Newport County).
46:49Corry Evans (Blackburn Rovers) wins a free kick in the defensive half.
46:21 BookingBooking Tom Lawrence (Blackburn Rovers) is shown the yellow card for a bad foul.
45:59Ben Davies (Newport County) wins a free kick in the defensive half.
45:59Foul by Tom Lawrence (Blackburn Rovers).
45:19Ben Davies (Newport County) wins a free kick in the defensive half.
45:19Foul by Tom Lawrence (Blackburn Rovers).
45:00Second Half begins Newport County 1, Blackburn Rovers 1.
45:00 SubstitutionSubstitution Substitution, Blackburn Rovers. Jordan Rhodes replaces Elliott Bennett.
45:00 +5:05 Half timeHalf Time First Half ends, Newport County 1, Blackburn Rovers 1.
45:00 +3:06Attempt missed. Mark Byrne (Newport County) right footed shot from outside the box is just a bit too high from a direct free kick.
45:00 +2:05Scott Barrow (Newport County) wins a free kick in the attacking half.
45:00 +2:05Foul by Elliott Bennett (Blackburn Rovers).
43:27Scott Barrow (Newport County) wins a free kick on the left wing.
43:27Foul by Ben Marshall (Blackburn Rovers).
40:40Offside, Blackburn Rovers. Ben Marshall tries a through ball, but Grant Hanley is caught offside.
40:05Foul by Mark Byrne (Newport County).
40:05Hope Akpan (Blackburn Rovers) wins a free kick in the attacking half.
38:32Offside, Blackburn Rovers. Ben Marshall tries a through ball, but Elliott Bennett is caught offside.
36:10Connor Dymond (Newport County) hits the left post with a right footed shot from the centre of the box. Assisted by Mark Byrne with a cross.
34:57Aaron Collins (Newport County) wins a free kick in the attacking half.
34:57Foul by Grant Hanley (Blackburn Rovers).
31:25Attempt missed. Aaron Collins (Newport County) right footed shot from outside the box is too high. Assisted by Andrew Hughes with a headed pass.
29:59 Goal scoredGoal! Goal! Newport County 1, Blackburn Rovers 1. Mark Byrne (Newport County) right footed shot from outside the box to the top right corner. Assisted by Danny Holmes.
26:29Offside, Newport County. Scott Boden tries a through ball, but Aaron Collins is caught offside.
25:50Scott Boden (Newport County) wins a free kick in the defensive half.
25:50Foul by Ben Marshall (Blackburn Rovers).
24:52Offside, Newport County. Mark Byrne tries a through ball, but Scott Boden is caught offside.
24:12Offside, Blackburn Rovers. Thomas Spurr tries a through ball, but Tom Lawrence is caught offside.
22:39Attempt missed. Chris Taylor (Blackburn Rovers) header from the centre of the box is high and wide to the right. Assisted by Elliott Bennett with a cross.
21:06Attempt missed. Ben Marshall (Blackburn Rovers) right footed shot from outside the box misses to the left following a corner.
20:27Corner, Blackburn Rovers. Conceded by Janoi Donacien.
18:09Corner, Newport County. Conceded by Jason Steele.
18:08Attempt saved. Mark Byrne (Newport County) right footed shot from outside the box is saved in the top centre of the goal.
18:05Attempt missed. Scott Barrow (Newport County) left footed shot from the left side of the box is close, but misses to the right.
16:51Foul by Darragh Lenihan (Blackburn Rovers).
16:51Tom Owen-Evans (Newport County) wins a free kick on the left wing.
13:05Delay over. They are ready to continue.
13:04 SubstitutionSubstitution Substitution, Newport County. Tom Owen-Evans replaces Medy Elito because of an injury.
9:24 DismissalDismissal Chris Brown (Blackburn Rovers) is shown the red card for violent conduct.
9:02Delay in match Medy Elito (Newport County) because of an injury.
8:40Foul by Chris Brown (Blackburn Rovers).
8:40Medy Elito (Newport County) wins a free kick in the defensive half.
7:13 Goal scoredGoal! Goal! Newport County 0, Blackburn Rovers 1. Ben Marshall (Blackburn Rovers) converts the penalty with a right footed shot to the bottom right corner.
6:21Penalty conceded by Scott Barrow (Newport County) after a foul in the penalty area.
6:21Penalty Blackburn Rovers. Ben Marshall draws a foul in the penalty area.
4:19Attempt missed. Chris Brown (Blackburn Rovers) header from the left side of the box is high and wide to the left. Assisted by Thomas Spurr with a cross.
1:45Medy Elito (Newport County) wins a free kick in the attacking half.
1:45Foul by Corry Evans (Blackburn Rovers).
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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