The capital club's third league win in a row helped them leapfrog Olympique de Marseille into second spot, with 47 points from 23 games.
Lyon travel to fifth-placed Monaco on Sunday and Marseille host Evian Thonon Gaillard on Saturday.
Sweden striker Zlatan Ibrahimovic, who has scored only one league goal since the turn of the year, produced another disappointing display but Lavezzi shone at the Parc des Princes.
The former Napoli forward poked the ball home from fellow Argentine Javier Pastore's pass in the 29th minute, giving PSG the lead after a sluggish start.
Home keeper Salvatore Sirigu was then forced into a low save to his right to deny Abdoulaye Doucoure's shot from just outside the box five minutes later.
Two minutes into the second half PSG came close to doubling their advantage but Edinson Cavani just failed to convert Marquinhos's cross.
The Uruguay striker missed another chance two minutes later when his low shot was saved by Benoit Costil.
Lavezzi then made a mistake that could have been costly, losing the ball to give Rennes a counter attacking opportunity but Sirigu saved from Christian Bruls.
Rennes stayed 10th on 30 points.
(Reporting by Julien Pretot, editing by Tony Jimenez)
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