Messi came on off the bench after 66 minutes, replacing Neymar.
Mbappe -- who could be appearing in one of his final matches for PSG with Real Madrid chasing him before the end of the transfer window -- had already put PSG two goals ahead with a strike in each half.
He scored his first goal on 16 minutes with a header from close range after Angel Di Maria floated a ball into the box.
PSG held the upper hand for much of the game but failed to capitalise on it. Their lack of finesse in their final shots nearly came back to bite them on 51 minutes when Marshall Munetsi put the ball into PSG's net after poor goalkeeping from Keylor Navas.
The ball was dropped into the box and El Bilal Toure hit it towards goal. Navas fumbled the ball into Munetsi's path and he stuck it into the net. However, after a VAR review it showed that he was marginally offside and the goal was disallowed.
However, PSG began to attack with a renewed energy and they found their second goal. Achraf Hakimi sent a cross to the back post on 63 minutes where Mbappe was once again waiting to convert.
The result means PSG have maintained their perfect Ligue 1 record this season and top the table with 12 points.