Julian Draxler put PSG ahead and Thomas Lemar levelled for Monaco before a goal from Angel Di Maria and a double from Edinson Cavani sealed a lively encounter at Parc OL.
PSG, who trail Monaco by three points in Ligue 1 with eight games left in the season, are now unbeaten in the French League Cup since a quarter-final defeat against St Etienne in November 2012.
Unai Emery's PSG looked nothing like the team who were knocked out of the Champions League by Barcelona with an embarrassing 6-1 defeat, while Monaco's French prodigy Kylian Mbappe put on a disappointing display.
"After what happened against Barca we had to win this final," said Di Maria.
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PSG midfielder Adrien Rabiot said they had a point to prove against the Ligue 1 leaders.
"We played a great game. Everybody said everywhere that Monaco were the favourites, that they were the best team in France. We showed who we were tonight," he said.
PSG, who were without injured centre back Marquinhos, started brightly.
Marco Verratti found Di Maria in the box with a splendid through ball and the Argentine, facing keeper Danijel Subasic, played a short pass to Draxler who tapped in to put PSG in front after four minutes.
Monaco, who missed the suspended Fabinho and the injured Radamel Falcao, struggled to create chances but equalised at the end of a superb move in the 27th minute.
Bernardo Silva took two defenders out of the game with a lobbed pass for Sidibe, who set up Lemar just on the outside of the box, and the midfielder curled a superb shot into the top corner.
PSG, however, made the most of another defensive mistake by Monaco as Di Maria beat the offside trap to collect Draxler's pass and beat Subasic one minute before halftime.
Cavani extended the lead nine minutes into the second half with a fine volley from Verratti's perfect cross from the right.
The Uruguay striker missed the target minutes later, before Di Maria's curled shot was also parried away by Subasic as PSG came close to a fourth goal.
That finally came in the last minute, when Cavani fired home from close range from Di Maria's cross from the left to hand PSG their seventh League Cup title with his 40th goal in 40 competitive games this season.
(Writing by Julien Pretot; Editing by Toby Davis)
