Mauricio Pochettino's side headed into Sunday's (AEDT) meeting on an 11-game unbeaten league run, albeit with four draws in its past five, and was ahead when Mbappe struck in the 32nd minute.
That strike was the 23-year-old's 10th in Ligue 1 this term, meaning he has hit double figures in six straight seasons – in the same period, no other player has done so more than three times.
Kehrer extended PSG's advantage after the interval as the hosts coasted to three points to move 11 clear of second-placed Nice at the summit.
Irvin Cardona twice forced smart stops from Gianluigi Donnarumma in the opening stages, while Mbappe drilled narrowly wide at the other end.
But there was no stopping Mbappe after 32 minutes when he fired through Brendan Chardonnet's legs and into the bottom-left corner, before Mauro Icardi saw his header disallowed for an apparent foul on Marco Bizot.
Marco Verratti almost added a second immediately after the break, only to be denied by the post, though the hosts doubled their lead soon after.
Nuno Mendes danced past Ronael Pierre-Gabriel to find Kehrer, who applied a first-time finish into the top-right corner from near the penalty spot.
Bizot then denied Marquinhos with a fantastic reflex save before making two fine stops from Mbappe to keep the scoreline respectable for Brest.
Another bright spot for PSG was another appearance for Sergio Ramos, the former Real Madrid defender slowly making his way back to regular football.