The first half was a static affair, with the Parisians pushing forward sporadically. Nene played a threatening ball to Jeremy Menez, who struggled to get free of Chris Mavinga, but the defender eventually made an excellent block to stop the Frenchman's shot giving the hosts the lead.
Soon after, Ancelotti's men had appeals for a penalty waved away when the ball appeared to strike Kevin Theophile-Catherine on the arm, but replays showed that the referee had made the correct decision.
PSG continued to push for an opener, and were inches away from breaking the deadlock seconds later when Menez bent an effort just wide of the post.
However, after a frantic opening, both teams died down. Menez dragged another effort wide of goal after a cunning one-two with Nene, before the former Roma man crumbled on the edge of the box, only to be told to get up by the official.
At the other end, Rennes offered very little, except on one occasion when Mavinga wriggled clear of his marker and Youssouf Hadji, who took a poor touch when well-stationed on the penalty spot.
On the stroke of half-time, controversy struck yet again as Nene picked up a booking for diving, when replays showed that he had been tripped.
Shortly after the restart, however, the match burst into life. Javier Pastore won the ball in midfield and sprayed a ball to Menez on the left wing. The 25-year-old beat his marker and pulled the ball back to Nene who kept his cool and put his side ahead.
Going behind only managed to rouse the visitors into action. Julien Feret fed Jires Kembo, who drove an effort wide, before Jonathan Pitroipa was felled by Blaise Matuidi and Zoumana Camara, only to see his appeals for a penalty waved away.
However, Rennes soon sank. Menez tore upfield, and was felled by Onyekachi Apam on the edge of the box. Nene stepped up and curled the ball past Benoit Costil and into the net.
Seconds later, the lively Menez was tripped in the penalty area by Jean-Armel Kana-Biyik, and Nene sent Costil the wrong way to complete his hat-trick from the spot.
With cries of "Ole" ringing out around Parc des Princes, PSG tried to play keep ball, but they were unable to stop Rennes from having a few shots in anger.
Kembo sent an effort straight into Salvatore Sirigu's grateful hands, before Victor Montano stung the former Palermo 'keeper's hands with a ferocious effort from distance.
Kana-Biyik knocked a Sirigu long ball straight into Menez's path, but his blushes were spared when his France international's shot bounced off the post.
In the end, however, three goals was more than enough for the Parisians to storm to victory, and remain in the hunt for Ligue 1 glory, but Montpellier's late win over Lille means that they need just a point from the final round of fixtures to clinch the title.