Sevilla, who won the first leg 2-0, went behind early in the game to a Philippe Coutinho penalty and never recovered.
Messi returned to the starting eleven and helped the Catalan giants secure a memorable win, in a game where he recorded his 50th Copa del Rey goal.
Barcelona’s desire to win the competition had been questioned after their first leg defeat, but Messi put those accusations to bed after their performance on Wednesday.
“It was said that we were throwing the cup or that we didn’t want it,” Messi said.
“My message was misunderstood: we will fight in three competitions, as is our obligation.
“At Barcelona, we fight for everything.
“Before the goal I had a couple of chances that I missed.
“But they [his teammates] scored others and when mine came, everything was decided.
“The team played great and we’re into the next round.”
It was also an important night for Coutinho, with the Brazilian getting on the scoresheet twice.
The 26-year-old midfielder has been under pressure to improve his performances after only recording two assists and four goals so far this season after his £142million move to the Nou Camp last January.
And it was Messi who helped Coutinho get off the mark by giving him Barcelona’s first penalty, which he gladly converted after 13 minutes.
Messi claims he allowed Coutinho to take the spot-kick after the Brazilian revealed a desire to take it.
“He took one against Levante and he wanted to take it,” Messi said.
“We spoke about it, he took it and I’m happy because that’s where everything started.”
Ivan Rakitic scored Barca’s second to tie the aggregate score at half time, with Coutinho heading in a third and Sergi Roberto finding the net to give the Catalan giants a 4-2 lead.
Guilherme Arana got one back for Sevilla, but goals from Luis Suarez and Messi sealed the win for Barca.
Valencia, Real Betis are also in the draw with Barcelona for the semi-finals and the last spot will be decided on Thursday between Real Madrid and Girona. Los Blancos hold a 4-2 lead from the first-leg.