Luis Suarez scored an early opener in the quarter-final second leg before Messi's deflected effort gave Barcelona a 2 -1 aggregate advantage as the holders overturned a 1-0 deficit from last week's first leg.
Messi had missed a penalty in that match as the leaders of La Liga were beaten for the first time since August, but they did enough on Thursday to join Sevilla, Valencia and Leganes in Friday's draw for the last four.
The 25-year-old Brazilian was introduced midway through the second half in place of Andres Iniesta, entering the Camp Nou pitch to a huge roar from the home crowd.
By that point Ernesto Valverde's men had already turned the tie around against the club for whom Coutinho played on loan from Inter Milan in 2012.
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"We are placing a lot of hope in Coutinho," said Valverde.
"He is going to do well for us in the game. He can help us because he knows how to create, he's good in the one-on-one situations. He is also a player who's able to see the free man. We know he can be a danger with a shot or a decisive pass. I think he made a good start."
The Uruguayan has now scored seven times in Barcelona's last six matches. Messi scored in the 25th minute, his shot beating goalkeeper Pau Lopez with the help of a sizeable deflection off Brazilian defender Naldo.
It was Barcelona's 4,000th goal at the Camp Nou in an official game.
Barcelona, who have won the Copa del Rey in the last three seasons, had a host of chances to put the tie to bed but saw out the victory, with Espanyol unable to get the away goal that would have swung the tie.
Valencia beat Alaves on penalties while Sevilla beat Atletico Madrid 3-1 on Tuesday for a 5-1 aggregate success.