Results elsewhere were kinder to Brest, with Nantes' 2-1 loss to Montpellier sparing them participation in the relegation play-off.
PSG's title hopes took an early blow when Jonathan David gave Lille the lead at Angers and Neymar then spurned a 19th-minute penalty after Faivre's rash foul on Angel Di Maria.
Brest goalkeeper Gautier Larsonneur engaged in some kidology by standing near his right-hand post for the kick and Neymar duly rolled his shot past the other upright.
Di Maria took matters into his own hands before half-time, albeit with a huge slice of fortune, when his right-wing corner deflected off Faivre and looped beyond Larsonneur.
Brest might have gone in level, only for Steve Mounie to power a close-range header over from Brendan Chardonnet's cross.
News of Lille's comfortable position perhaps informed the lack of intensity at the start of the second half, with PSG creating little of note from open play and Di Maria rippled the side-netting with a free-kick.
Mounie erred again when he burst clear of a haphazard visiting backline in the 65th minute, shooting at Keylor Navas' legs.
PSG were indebted to Navas once more soon afterwards, the former Real Madrid man's positioning impeccable when Gaetan Charbonnier met Mounie's knockdown.
Mbappe had existed on the fringes of the contest but was alert to round Larsonneur in the 71st minute and kept his composure to finish after being bundled to the floor by Jean-Kevin Duverne in front of the unguarded net.
Larsonneur denied substitute Mauro Icardi and Mbappe as Brest appeared increasingly forlorn – their fate ultimately saved by others.