The Brazilian shot low across goal with 20 minutes left as Liverpool finally broke down Gary Bowyer's resolute home side, who had earned a replay with a gritty 0-0 draw at Anfield.
Blackburn battled bravely, and they caused brief late panic when goalkeeper Simon Eastwood was sent forward for a corner in injury time.
But they could not deny the Premier League side, as Brendan Rodgers' search for a first trophy as Liverpool manager remained on course.
Visiting goalkeeper Simon Mignolet played his part as he kept out a shot from Tom Cairney and then turned a Ben Marshall header onto the post early in the second half.
Eastwood, though, was by far the busier - and had kept his side in the game in the first half with saves from Glen Johnson and Coutinho.
Joe Allen wasted Liverpool's first opening after four minutes when, having got to the ball first on the edge of the Blackburn area, his shot was well wide.
Raheem Sterling also tried his luck as Liverpool pressed early on, but his effort flew over.
Blackburn's first real attack came after 13 minutes when Mamadou Sakho left the ball for Liverpool goalkeeper Mignolet but was forced to race back to block Craig Conway's shot.
Daniel Sturridge - recalled to the starting line-up in place of Lazar Markovic - shot narrowly over as Liverpool continued to dominate, before the England striker failed to control Jordan Henderson's long ball.
Jordan Rhodes then got in front of Dejan Lovren at the other end after 25 minutes, but he headed over with a rare Blackburn chance.
An injured Sakho could only watch that attack, and the limping defender was soon substituted by Kolo Toure, in the absence of suspended Martin Skrtel.
Johnson forced a good save out of Eastwood on the half-hour mark after the defender's initial cross had come back to him, before Eastwood again got down well to turn Coutinho's low shot through a crowd of players and around the post.
But Blackburn began the second half with more purpose and Mignolet was forced to turn Cairney's shot out for a corner before, from the resulting flag kick, the Belgian pushed Marshall's header onto the post.
Corry Evans then tested Mignolet with a shot 10 minutes into the second half, as Blackburn continued to force the pace.
Just after the hour, Bowyer brought on Rudy Gestede - who was restricted to a role on the bench because of a hamstring injury - and in his first moment of action, the striker played through Rhodes, whose shot was blocked by Toure.
Finally, with 20 minutes to go, Coutinho broke the deadlock with a moment of magic. The Brazilian took a return pass from Henderson in his stride and fired low into the opposite corner from the edge of the six yard area.
There was almost late drama when, in injury time, Blackburn threw goalkeeper Eastwood forward for a corner and he caused panic as Liverpool somehow survived to book their semi-final against Villa at Wembley.
