Angel Di Maria scored twice after an early opener from Italian striker Moise Kean, who joined a long list of injured players, leaving coach Thomas Tuchel without all of his main forwards except the Argentine.
Rennes stay third on 18 points.
Kean scored his third Ligue 1 goal in four games to put the hosts ahead in the 11th minute with a cross-shot after being set up by Di Maria, who benefitted from sloppy play by Rennes.
PSG, already without injured Neymar, Kylian Mbappe, Presnel Kimpembe, Mauro Icardi, Marco Verratti, Julian Draxler, Juan Bernat and Pablo Sarabia, suffered more woes when Idrissa Gueye limped off the pitch to be replaced by Rafinha one minute later.
Kean limped off the pitch shortly before the hour and was substituted for defensive midfielder Danilo Pereira.
Di Maria was at it again in the 73rd, adding the third goal with a deflected shot against the run of play.