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After an even first half Liverpool dominated the second period but wave after wave of attack was thwarted by a Blackburn side who had already accounted for Premier League sides Swansea City and Stoke City in the two previous rounds.
Kolo Toure headed against a post, while Daniel Sturridge, Philippe Coutinho and Raheem Sterling failed to break down their second tier visitors despite relentless pressure.
Aston Villa -- who beat West Bromwich Albion 2-0 on Saturday -- are the only side to seal a semi-final spot so far while Manchester United host holders Arsenal on Monday.
Giant-killers Bradford City travel to Reading on Mar. 16 for a replay after their 0-0 draw.
"It was 90 minutes of concentration because they had a lot of the ball and they had some great players out there," Blackburn captain Matthew Kilgallon told BT Sport.
"It was just about concentration and working for each other.
"Massive games like this you really enjoy and they're the ones you tell people about when you finish (playing)."
While third tier Bradford had captured the imagination with their storied march to the quarter-final, Blackburn had gone about their business quietly in dumping out Swansea and Stoke before they arrived at Anfield.
Pre-match renditions of 'You'll never Walk Alone' had barely ended when Liverpool lost their defensive rock Martin Skrtel.
The Slovakia defender contested a header against Blackburn's Rudy Gestede but fell heavily on his neck and, after an eight-minute delay, was carried off on a stretcher.
Liverpool had lost just one of their previous 21 games in all competitions but Blackburn coped comfortably in the opening stages and led by the powerful Gestede were carving out opportunities of their own.
Craig Conway spurned the best chance of the opening period, blazing high and wide from close-range.
Sturridge's rasping shot in first half stoppage time drew a smart stop from Blackburn keeper Simon Eastwood.
Immediately after the break the hosts were indebted to goalkeeper Simon Mignolet who produced a wonderful save to palm away Alex Baptiste's bulleted goal-bound header but thereafter Liverpool were dominant.
Toure hit the post and Sturridge became increasingly influential though he was thwarted by Blackburn's determined rearguard. Mario Balotelli was introduced midway through the half but was restricted to speculative long-range efforts.
Liverpool laid siege to Blackburn's goal in the closing stages but failed to force Eastwood into many meaningful saves. (Reporting By Tom Hayward; editing by Martyn Herman)