PSG won on penalties after the match had finished 1-1 following extra-time.
PSG struck first in the 38th minute through Khvicha Kvaratskhelia. Flamengo responded after the break as Jorginho converted a penalty on 62 minutes.
In the shootout, PSG goalkeeper Matvey Safonov produced an amazing four saves to secure the Cup for the French giants.
"To be honest, we saw a very good match, against a Flamengo team that plays very well. It was very difficult, but the quality and mentality of the players were there, and seeing that spirit was a real pleasure against a very good team," said Luis Enrique afterwards.
The PSG coach also commented on the flow of the game.
"We had a very good first half, we controlled it well, we were able to press our opponent, but after the penalty, it became more balanced and more difficult. I must congratulate Flamengo not only for today's match, but also for their season," he added.
On Fla coach Filipe Luis, Luis Enrique also said: "Of course he has the level to coach in Europe and at any club in the world.
"He is still very young, but his teams will continue to play beautiful football."