Julian Draxler fired PSG ahead with just four minutes played in the final in Lyon, but Thomas Lemar levelled for Monaco before the half hour.
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Argentine international Di Maria restored the lead for Unai Emery's side a minute before half-time and Edinson Cavani sealed a record seventh title for PSG with a clinical second-half brace.
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"We've had some difficult times, but we haven't given up. We've proved we're a great side. I think it's a deserved win and we can celebrate a bit," midfielder Marco Verratti told Canal+. "In four years here we've won everything. We have a great team and this is a victory for everyone involved. The league title is our goal now and we'll give it our all until the finish."
After the shock of their Champions League last 16 collapse against Barcelona in the second leg, a third meeting with Ligue 1 leaders Monaco this season presented an opportunity for redemption for PSG.
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Monaco's Radamel Falcao failed to shake off a nagging hip injury that has sidelined the Colombian since March 11, but Thiago Motta returned to the PSG line-up for his first start in six weeks.
PSG have dominated the competition in recent seasons -- Monaco's last major trophy came when they won the 2003 final -- and the holders stormed into an early lead albeit in controversial circumstances.
Verratti slipped Di Maria in behind the defence, with the Argentine electing to unselfishly slide the ball across for Draxler to tap home.
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Replays showed the Germany international was marginally offside, although unlike in Tuesday's international between France and Spain where a video assistant referee was used in the country for the first time there was no such help available at Parc OL.
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Monaco shrugged off that setback as Lemar replied with a fine equaliser on 27 minutes.
Bernardo Silva's chipped pass found Djibril Sidibe inside the area and the France full-back laid the ball back for Lemar to expertly sweep home from the edge of the box.
Cavani thought he had put PSG back in front as he reacted quickest to Thiago Silva's towering back-post header, but the Uruguayan's goal-bound flick was superbly kept out by Danijel Subasic before the Croat smothered the rebound.
However there was nothing the Monaco keeper could do as Di Maria stabbed low into the corner with half-time approaching after Draxler displayed remarkable balance to feed the unmarked Argentine.
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Joao Moutinho fizzed a shot just over the crossbar following the interval, but PSG landed the fatal blow on 54 minutes as Cavani hammered past Subasic after a sublime floated cross from Verratti.
Benjamin Mendy went close to halving the deficit with a stinging effort, but Cavani should have netted his second and sealed the outcome when he steered wide from Di Maria's delivery from the left.
Substitute Irvin Cardona flashed a header just wide of Kevin Trapp's left-hand post, while Subasic dived at full-stretch to palm away a Di Maria effort with the outside of the boot.
But the Argentine combined with Cavani in the final minute to add a fourth for PSG as the Uruguayan powered home Di Maria's cross from close range to cap a convincing triumph.
"We played a great match, with humility, consistency and sacrifice," said Cavani.
Monaco boss Leonardo Jardim commented: "For several of our young players this was their first final. Just because we lost doesn't mean we will play less well in the competitions still open to us."
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