The Catalans were trailing at the Nou Camp due to Javier Pastore's opener and brought on their Argentine talisman, who was benched due to a hamstring injury, with 28 minutes remaining.
Although Messi could not add to his tally of eight Champions League goals, he added a spark to Barca's attack and it was his run that began the move which saw Pedro equalise on 70 minutes to claim a 3-3 draw on aggregate.
David Villa, who received the ball from Messi and laid it off for Pedro, told Canal Plus: "Messi is the best player in the world and he changed the game just by being on the pitch.
"We have to congratulate him for his show of commitment to the team and to football."
Villa who began the match in attack alongside Cesc Fabregas and Pedro, added: "It is thanks to him that we have qualified.
"We are delighted to qualify after suffering so much. They caused us a lot of problems, and they did a lot of damage with their counter-attacks," he said.
"We gave the ball away a lot, which we don't normally do, we didn't play well. We knew that they [PSG] were strong on the counter-attack but they still made it difficult for us. However, we have qualified, and that's what's important."
Gerard Pique, who came through Barca's youth ranks with Messi, said the Blaugrana had no choice but to bring him on.
"In Leo we are talking about the best player in the world and when things are not going well you have to use him," he said.
"Even if he is half lame, his presence on the pitch is enough to lift us and our play in general."
Wing-back Dani Alves added: "That's the power he has, and that's why he's the best player in the world. His mere presence gave the whole match a different atmosphere.
"We're just happy to have him as a team-mate, I'd rather have Leo than any other player."
Barca assistant coach Jordi Roura agreed Messi changed the game, and said it was always their plan to bring him on if the game was not going to plan.
"We had agreed that he would play from the moment things started to go wrong for us, and that moment arrived. He came onto the pitch and once again participated in a goal," he said.
"He proved his competitive edge, he's an irreplaceable player."
The draw for the semi-finals is on Friday, with possible opponents arch rivals Real Madrid, last year's runners-up Bayern Munich and the side they displaced as German champions at the weekend, Borussia Dortmund.
"It feels like it's a duel between the Spanish and German leagues and I really have no preference," Barca sporting director Andoni Zubizarreta said.
"For better or for worse, we showed that like a Manchester United or a Bayern Munich, we can make it through whether we are playing poorly or playing well," added the former Barca and Spain goalkeeper.