Mbappe made his farewell appearance for PSG before an expected move to Real Madrid but he was unable to add to his club-record tally of 256 goals with Ousmane Dembele and Fabian Ruiz scoring on the night.
Dembele and Ruiz netted in the first half and PSG then withstood a Lyon comeback attempt after the break following a Jake O'Brien goal which reduced the deficit.
The most successful side in the history of the French Cup, PSG have now won the trophy 15 times, including seven times in the last decade and four since Mbappe signed from Monaco as a teenager in 2017.
The victory allowed PSG to complete a domestic league and cup double in Luis Enrique's first season as coach, although the campaign remains overshadowed by their exit from the Champions League in the semi-finals against Borussia Dortmund.
"We played the final very well. We played with great intensity and were great on the ball," said Luis Enrique.
"I think we have had a very good season. We would have liked to stay around for another week and not go on holiday yet but that is life," he said, referring to next weekend's Champions League final.
"Nobody said football was fair, but it doesn't matter. Next season we will come back stronger and will look to sign even hungrier players, who have even more desire to win."
Of the departing Mbappe he added: "I think I have been lucky to coach Kylian but it has been a difficult season for him because after seven years and all he has achieved it is always hard to say goodbye.
"But he was always prepared to help the team and tonight was the cherry on the cake even if he didn't score."
Clashes between supporters
The game was somewhat overshadowed by incidents earlier in the day, with rival fans clashing at a motorway toll around 50 kilometres south of the northern city of Lille.
The clashes involved about 100 Lyon supporters and about 200 PSG fans, with two coaches ending up on fire, according to a police source.
A source in the regional police authorities said 20 supporters were slightly injured, with French President Emmanuel Macron, who attended the final, condemning the violence.
Mbappe was making his 308th and final appearance for his hometown club, for whom he signed in August 2017 from Monaco in a 180 million-euro deal.
Victory means he leaves PSG with four French Cup winners' medals to go with six Ligue 1 titles and two victories in the now-defunct League Cup.
Mbappe finished his last season in Paris with 44 goals in all competitions, eight on PSG's run to the Cup final.
He was centimetres away from giving PSG an early lead at Lille's Stade Pierre-Mauroy, which was hosting the game with usual venue the Stade de France being prepared to host the Olympics.
A second-minute corner was headed on by Lucas Beraldo and Mbappe, diving in at the far post, narrowly failed to connect with the ball.
Lyon survived an early onslaught but fell behind midway through the first half when Dembele was left completely unmarked at the back post to head in a cross.
Dembele turned provider as PSG scored again in the 34th minute, when his ball to the back post was converted at the second attempt by Spain midfielder Ruiz.
Lyon, who enjoyed a remarkable revival in Ligue 1 to go from bottom of the table in December to finish sixth and qualify for Europe, appeared down and out.
They did attempt a comeback, with Irish defender O'Brien heading in a corner 10 minutes after the break to give them hope.
But PSG goalkeeper Gianluigi Donnarumma produced a brilliant save to tip a Nicolas Tagliafico header over the bar, and Alexandre Lacazette had a shot deflected wide as Mbappe and PSG held on.
"We have mixed feelings tonight," said Lyon coach Pierre Sage.
"If you had told us at the start of December that we would qualify for Europe through the league and get to the Cup final, I don't think anyone would have believed it."
