The Brazilian collected a Jordan Henderson though ball to rifle low into the net midway through the second half.
Ben Marshall had Blackburn’s best chance parried onto the post when he headed a corner towards goal, seconds after Simon Mignolet had blocked Tom Cairney’s ranged shot.
And the goalkeeper himself had a last-gasp turn and shot saved from his opposite number as Rovers threw men forward late on but to no avail.
But the Reds showed greater intent going forward, with Daniel Sturridge twice seeing efforts saved, while Coutinho forced a scrambling parry from Simon Eastwood.
Unfortunately for manager Brendan Rodgers, he was handed another injury headache when Mamadou Sakho limped out with a hamstring strain and now looks a doubt for their Premier League clash with Newcastle this weekend.
Liverpool must overhaul a seven-point deficit if they are to qualify for the Champions League next season and require victory over the Magpies before facing fellow FA Cup semi-finalists Aston Villa at Wembley.
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