PSG suffered its sixth league loss of the campaign at home to Monaco last weekend but was good value for this win at Stade Gaston-Gerard.
Mbappe tucked away a penalty, awarded for handball against Bersant Celina, after Kean had opened the scoring for the reigning champion with his 15th goal of the campaign.
Prolific forward Mbappe doubled his tally in the second half and Danilo Pereira headed in a late fourth to help PSG move to within a point of leaders Lille, which plays its game in hand at home to Strasbourg on Monday (AEDT).
Dijon had failed to keep a clean sheet in its previous 11 top-flight meetings with PSG, losing 10 of those, and was behind inside six minutes of this latest encounter.
Kean feinted one way and opened up his body before picking out the bottom-right corner with a poked finish from seven yards to maintain his good run in front of goal.
PSG added a second just past the half-hour mark through Mbappe's composed penalty after Thilo Kehrer's powerful drive hit the outstretched hand of Celina inside the box.
Julian Draxler had a goal disallowed before half-time for offside against Mbappe in the build-up but the latter scored with a fine first-time finish five minutes into the second half.
Mauricio Pochettino's men had another Draxler strike ruled out after the attacker timed his run a little too early, while Pablo Sarabia had a shot saved, but Danilo climbed highest to nod in his first goal for the club eight minutes from time.