It was the capital club’s ninth French Cup title and moves them within one of the record held by bitter rivals Olympique de Marseille.
The French Cup was the only domestic title missing from PSG’s cabinet since they were taken over by their big-spending Qatari owners in 2011.
PSG were without the suspended Javier Pastore and the Argentine playmaker was missed as Laurent Blanc’s side looked short of ideas at a packed Stade de France.
Blanc decided to pick Brazil centre back Thiago Silva, who had been doubtful with a thigh injury, but his players were not at their best and Zlatan Ibrahimovic was out of sorts as well.
PSG’s first clear chance came five minutes from the interval when Thiago Motta’s fierce strike smashed against the post.
The French champions finally broke through 20 minutes into the second half when Cavani nodded Gregory van der Wiel’s cross past Donovan Leon.
“We had a great, great season. What we managed to do is unique. We play at PSG to live such moments,” midfielder Blaise Matuidi said.
“We may have some regrets from the Champions League but we lost to an ogre (Barcelona).”
“It’s also important to pay proper tribute to Auxerre who played a good game and caused us some trouble.
“It’s been a long season but, in the end, we achieved something special. We have amazing players and we’re very happy with what we’ve done. Now is time to celebrate.”