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Carroll, who has scored just nine goals since his 35 million pound move from Newcastle United in January last year, headed home from six metres out with only three minutes on the clock to worsen Blackburn's plight.
Maxi Rodriguez scored in the 13th and 16th minutes for Liverpool.
Blackburn remained in the bottom three on 28 points from 33 games, level on points with 17th-placed Queens Park Rangers and Wigan Athletic who have both played one fewer match, while Liverpool stayed eighth on 46 points.
Leaders Manchester United (79 points) visit second from bottom Wigan on Wednesday when second-placed Manchester City (71) host mid-table West Bromwich Albion and Arsenal (61), in third, travel to bottom club Wolverhampton Wanderers.