Mbappe fired home from a Lionel Messi assist in the third minute of added time at the Parc des Princes having earlier seen a deflected strike come back off the post and been denied a goal by the tightest of offside calls.
The result allows PSG to stretch their huge lead at the top of the French table to 16 points before second-placed Marseille play at Metz on Sunday.
However, the nature of the performance from Mauricio Pochettino's side suggests they will struggle when Madrid visit for the first leg of their Champions League last-16 tie next Tuesday.
Apart from Mbappe's interventions, the evening was most notable for the decision by the 'ultra' groups who provide the most vocal support at the Parc des Princes to not take their seats until half an hour into the game.