Brendan Rodgers' men headed into the quarter-final tie with six wins from their last seven matches in all competitions.
But they endured a frustrating afternoon against their Championship opponents, creating little of note in the first half after their defender Martin Skrtel required extended medical attention following an aerial challenge with Blackburn frontman Rudy Gestede.
Kolo Toure, on in place of Skrtel, hit the post as Liverpool increased the pressure during the second period but they must now head to Ewood Park to maintain their hopes of giving club captain Steven Gerrard - an injury absentee once more on Sunday - a memorable Wembley send-off.
Skrtel landed heavily and momentarily lost consciousness following a second-minute aerial duel with Gestede and the Liverpool man left the field on a stretcher - gesturing positively to the crowd following a worryingly long period of treatment.
Gestede made his presence felt once more in the 13th minute, climbing powerfully to beat Simon Mignolet to the ball but heading wide.
Liverpool were still struggling for their usual fluency as Adam Lallana had a 19th-minute penalty claim rejected - Rovers defender Matt Kilgallon completing a risky last-ditch challenge.
Raheem Sterling got back to block Gestede as the striker wound up a volley, the ball striking the England man's hand but prompting no penalty appeal from Blackburn.
The clearest opening of the first half fell to the visitors in the 32nd minute as the impressive Gestede dummied cleverly for Craig Conway to slice wastefully off target.
Toure was caught out of position on that attack and he was soon involved at the other end, converting Daniel Sturridge's set-piece knockdown from an offside position.
Blackburn goalkeeper Simon Eastwood was under employed during the first half but reacted sharply to beat away a venomous shot on the turn from Sturridge during the seventh of eight minutes added on for Skrtel's injury.
It was announced on the Anfield public address system at half-time that the Slovakia international, who went to hospital for a precautionary scan, had suffered no serious damage but his team-mates still grasped unconvincingly for their best form when the action resumed.
Mignolet needed a save of the highest quality to keep out Alex Baptiste’s header from Conway's 49th-minute corner.
The game's latest marginal penalty shout arrived in the 55th minute as Kilgallon put his arm across Sturridge and the England striker went down. Again, referee Andre Marriner was unmoved.
Toure almost broke the deadlock as the hour approached, heading Philippe Coutinho's free-kick from the left into the turf and against the right-hand post.
In the 73rd minute, Baptiste misjudged a defensive header but Sturridge could only blast wide of the near post.
There was relentless Liverpool pressure during the closing stages but, aside from a save on the angle to deny Jordan Henderson in the 83rd minute, Eastwood was well protected.
As they did in round four after being held by Bolton Wanderers, Liverpool must now travel to a Championship club to progress, while Blackburn retain hopes of repeating their giant-killing feats of two seasons ago against Arsenal.
