Two goals in four minutes from Maxi Rodriguez saw Steve Kean’s side ripped apart at the back early on, but a straight red card for goalkeeper Doni after he brought down Yakubu saw the visitors reduced to 10 men with the striker having the resulting penalty kick saved by substitute Brad Jones.
Yakubu grabbed a goal back in the 36th minute and converted a second penalty attempt in a frenetic second half after he was pushed over by Jones, but Carroll clinched the three points for his side with a bullet header in added time to leave the hosts devastated as Liverpool ended a dismal run of form.
Embattled Kenny Dalglish made six changes to the side that drew 1-1 with Aston Villa on Saturday as Luis Suarez and Steven Gerrard were among those rested ahead of the FA Cup semi-final with Everton at the weekend; meanwhile, Rovers made two changes with Mauro Formica and Marcus Olsson replacing Jason Lowe and Morten Gamst Pedersen.
Both sides were desperate to arrest alarming slumps of form: Liverpool came into the match having won just one of their last nine league games, while Rovers had lost their last three successive matches.
Carroll, who was recalled after three substitute appearances in four matches, struggled early on as the home fans greeted every poor touch from the forward with ironic cheers, while David Hoilett looked dangerous at the other end.
Despite Rovers enjoying much of the early possession, it was the visitors who opened their account in the 13th minute: Martin Skrtel unleashed a raking long pass upfield to Craig Bellamy, who zipped down the right and drilled a low cross into the six-yard box for Rodriguez to tap the ball home.
The goal meant that Blackburn have now kept just one clean sheet in their last 18 Premier League games at Ewood Park.
Barely had the hosts had a chance to regroup before Liverpool doubled their lead. David Dunn gave the ball away sloppily in the Liverpool half before the visitors broke upfield superbly through Jonjo Shelvey, whose initial shot was blocked before Rodriguez slammed an emphatic finish into the net to double his tally.
Blackburn were undeterred and continued to press forward in search of a breakthrough as Hoilett latched onto a woeful backpass from John Flanagan and was put through on goal before being hauled down by Doni with a straight red card and a penalty following.
Jones was introduced as the hapless Flanagan made way, and the Australian’s first act was to comfortably save a dismal penalty attempt from Yakubu, who tried to be too cute with a soft side-footed effort to the keeper’s right. Blackburn have now missed four of their seven penalty kicks this season.
But the forward made amends in the 36th minute to reduce the deficit as he ghosted in unmarked to head beyond Jones from Dunn’s precise free-kick with his 15th goal of the season and his eighth in his last 10 games at Ewood Park.
A barrage of pressure ensued and Rovers were almost level four minutes later as Martin Olsson whipped over a stunning delivery from the left byline and fellow defender Grant Hanley came agonisingly close to turning the ball home from close range as the ball fizzed across the six-yard box.
Within just three minutes of the restart, Carroll squandered a glorious opportunity to restore Liverpool’s two-goal cushion as he stooped low to head wide from a Bellamy corner out on the left with just Robinson to beat from close range.
Shelvey produced another lung-busting run after he dispossessed Dunn in midfield and charged through on goal, but he proceeded to lose his composure and blaze a wild shot over the crossbar with Bellamy to his right, screaming for the ball.
Further drama followed as Jones inexplicably dallied on the ball and enabled Yakubu to charge the ball down before the goalkeeper pushed the forward over inside the box with the referee controversially deciding to show just a yellow card for the infringement.
Again, it was less than convincing, but Yakubu beat Jones with a penalty kick straight down the middle to level the scores with the Rovers players continuing to show their displeasure with referee Anthony Taylor’s decision to keep the substitute keeper on the field.
Carroll came perilously close to scoring an own goal in the 77th minute as he headed back towards his own net from a long ball from Robinson, only for Jones to spare his blushes by furiously back-peddling and turning the ball over the crossbar.
But the forward was clinical at the other end after a breathless final 10 minutes as he powered a bullet header beyond the helpless Robinson from close range to claim all three points for Dalglish's Liverpool in a dramatic finale.
The victory sees the Reds close to within a point of rivals Everton on 46 points, while Rovers remain in the relegation zone on goal difference having now played a game more than both QPR and Bolton.