The result left Brest in 13th place on 25 points.
At the Parc des Princes, PSG were missing Lionel Messi, who is still recovering from a COVID-19 infection, and had to cope with the last-minute absence of goalkeeper Keylor Navas, who tested positive for the novel coronavirus.
Brest, looking for their first top-flight win against PSG since 1985, had three shots on target in the opening 20 minutes.
It was Mbappe, however, who broke the deadlock in the 32nd with a clinical low shot from 16 metres for his 10th Ligue 1 goal of the season as PSG increased the pressure.
Marco Verratti came close to doubling the lead three minutes into the second half but his angled shot hit the post.
Kehrer and Mbappe, who was booked for a scuffle with Hugo Magnetti in the first half, had other chances but Mauricio Pochettino's side had already wrapped a routine victory.