Rovers' 2016 FA Cup campaign came to an end against an impressive West Ham United side at Ewood Park.
After a Victor Moses goal, a pair of strikes from Dimitri Payet and Emmanuel Emenike saw the Premier League side come from behind to reach the last eight of the competition.
It had started brightly for Rovers when Ben Marshall fired the home side in front on 20 minutes. But the Hammers soon levelled as Moses shot low under Jason Steele after his run went unchecked.
A Payet free-kick before the break saw the visitors lead, and although Rovers started the second half strongly with Marshall, Darragh Lenihan and Elliott Ward all going close, the sending off of Chris Taylor on 55 effectively ended any chance the home side would have of getting back into the game.
West Ham took full advantage as Emenike fired home from close-range, and whilst the Londoners would also end with ten men after Cheikhou Kouyate saw red, the top-flight high-fliers confirmed their credentials with further goals from Emenike and Payet to end Rovers' dreams of a place in the quarter-finals.
Paul Lambert made five changes for the highly-anticipated cup match, choosing to refresh the side that defeated Fulham so comfortably in midweek.
Elliott Ward, Adam Henley, Hope Akpan, Craig Conway and Chris Taylor were the men to come in, with Danny Graham cup-tied and Tommy Spurr missing with a knee injury. Grant Hanley, Jordi Gomez and Corry Evans all dropped to the bench.
There was plenty of endeavour on display in the opening exchanges, Rovers letting their top-flight opponents know that they would be in for a competitive cup tie.
Moses saw an early effort deflect wide of goal, whilst Akpan headed over an Elliott Bennett corner.
And it was from a Bennett corner kick that Rovers would take the lead on 20 minutes. His ball in from the right was cleared only as far Marshall, and he found the back of the net with the sweetest of strikes that gave Darren Randolph no chance.
The goal was Marshall's fourth in the competition this season, the defender having scored in every round for Rovers.
However the home lead would last just six minutes as the Hammers hit back straight away.
It was Moses who was given far too much time and space in the centre of the park and he wasted little time by advancing and beating Jason Steele with a low drive.
Boosted by getting back on level terms, Slaven Bilic's side pressed Rovers, putting the blue and whites under more and more pressure.
On 36 minutes Chris Taylor was booked for a tug on Payet and the Frenchman took full advantage. Superbly striking the resulting free-kick over the Rovers wall and into the top corner to turn the tie on it's head.
Rovers threatened to make it 2-2 on the stroke of half-time as Taylor intercepted a slack pass on halfway before racing into the penalty area, but Randolph smothered his shot.
It was Marshall with the first sight of goal as the second half resumed, the defender arriving to fire goalwards, but his low strike was easily claimed, then Darragh Lenihan was the next to try his luck but his well-struck effort flashed narrowly wide.
The home side continued to press as the two Rovers players then combined for another chance for an equaliser. Marshall's free-kick picked out the Irishman, but Lenihan's looping header was caught high by Randolph.
Excellent wing play by Adam Henley saw Rovers win a corner from which former Hammers' youngster Elliott Ward had a shooting chance, but Angelo Ogbonna made an important block.
But as Moses looked to turn defence into attack he was tripped by Taylor and with the midfielder having already been booked in the first half, referee Jonathan Moss wasted little time in showing him his second yellow followed by the inevitable red.
A goal to the good and now with a man advantage, West Ham looked to stretch their lead. Michail Antonio forced Steele into a fine near-post save, before slick passing saw Mark Noble race into the box but the Hammers captain dragged his shot wide.
Simeon Jackson was introduced with Conway making way, but it was the visitors who would grab the all-important fourth goal.
After Cheikhou Kouyate saw a goal chalked out for offside, Rovers failed to clear their lines once more, and West Ham wouldn't waste their opportunity a second time time as Antonio kept play alive before Emmanuel Emenike applied the finishing touch.
Moses was again given far too much time in space to invite another shot at goal which Steele saved low, before West Ham were then reduced to ten men themselves when Kouyate tripped Henley when through on goal.
But with Rovers pushing forward in search of a way back into the game, the visitors grabbed a fourth goal five minutes from time.
Victor Moses had been denied by Steele and Duffy, but it was Emenike who would grab his second of the game, beating the offside trap before rounding the Rovers keeper and finding the back of the net despite the best of efforts from Ward on the line.
Emenike could have had a hat-trick as Rovers were hit on the break once more, but on this occasion he could only fire against the outside of the post.
Emenike would then see an effort chalked off for offside before the impressive Payet added a fifth deep into injury-time. The Frenchman capping a fine display with his second of the game to ensure it would be West Ham's name into the quarter-final draw.
ROVERS: Steele, Marshall, Duffy (c), Ward, Henley, Taylor, Akpan, Lenihan, Conway (sub Jackson 59 mins), Bennett, Brown (sub Watt 78 mins).
Subs not used: Raya (GK), Kilgallon, Hanley, J, Gomez, Evans.
Goals: Marshall 20 mins
Booked: Taylor, Lenihan.
WEST HAM: Randolph, Cresswell, Kouyate, Obiang (sub Lanzini 67 mins), Noble (c) (sub Song 73 mins), Collins, Moses, Ogbonna (sub Oxford 78 mins), Payet, Emenike, Antonio.
Subs not used: Adrian (GK), Henry, Parfitt-Williams, Browne.
Goals: Moses 26 mins, Payet 36, 90+2 mins, Emenike 64, 85 mins.
Attendance: 18,793 (including 7185 visiting supporters).