Trailing 4-0 after the first leg in Paris, Barcelona won 6-1 at their Nou Camp stadium, with three late goals clinching an historic 6-5 aggregate victory.
Enrique had been criticised in Paris by midfielder Sergio Busquets, who said that PSG "were much better tactically than us; they had a plan and executed it", while Andres Iniesta said the heavy loss was "not down to attitude but due to football".
After Barca could only sneak past Leganes in their first game after the nightmare in Paris, Luis Enrique rejigged his formation from 4-3-3 to 3-4-3, employing Sergi Roberto as an extra midfielder when the team had the ball.
Roberto did not start the second leg, with Enrique opting for Brazilian midfielder Rafinha, but he came off the bench late in the second half to score the decisive sixth goal.
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The shift in shape has been one of the key factors behind Barca's recent resurgence as they beat Atletico Madrid 2-1 and hammered Sporting Gijon 6-1 and Celta Vigo 5-0 before the remarkable thrashing of PSG.
Gerard Pique highlighted his manager's role in the comeback, the first time any team has overturned a 4-0 deficit in a Champions League tie.
"I would like him more than ever to get mentioned on the front pages tomorrow because he did most of the work for this game with his plan and approach," the Barca defender said.
"If at other times he has been treated unfairly, today or tomorrow he deserves all the credit."
The coach was also praised in the Spanish media, with daily Marca describing his tactical preparation as "the perfect plan", while Sport highlighted "Luis Enrique's three decisions that made the comeback possible".
One of those decisions was the coach's announcement after the win over Sporting that he would not continue at Barcelona beyond the summer, removing any tension that existed between Enrique and the squad.
Enrique, who has won eight out of a possible 10 trophies as Barca coach and could claim another treble in his final season, has often declared to be unaffected by criticism. But after Wednesday's triumph he alluded to the negative press he received after the first leg.
"We had to go through a process of mourning first. Everyone came in for criticism, especially one person. I don't read the press but I hear about everything," he said.
"This is dedicated to all the Barca fans who believed in us. This marvellous sport always gives you a chance for revenge and we were able to have a unique night."
(Editing by David Goodman)
