Uruguay striker Cavani scored with a superb flicked finish midway through the first half to move to 155 goals – one behind Zlatan Ibrahimovic's record – and set Unai Emery's side up for a routine evening.
Mbappe, playing on his birthday, had showed an electrifying blend of pace and skill to set up Cavani for that goal before getting on the scoresheet himself after 57 minutes.
Wonderfully teed up by the impressive Argentinian midfielder Giovani Lo Celso, the France international coolly slotted home to continue his effortless start to life at the Parc des Princes.
Cavani missed a number of clear openings to add to this tally and will now have to wait until at least 8 January to pull past Ibrahimovic when the Paris giant takes on Rennes in the Coupe de France.
Yuri Berchiche drilled in a third after clever play from Neymar before Caen scored a late consolation when Ivan Santini netted from the penalty spot.