The win moves the champions above AS Monaco into first in the table, albeit only provisionally.
The away side had the first chance of the match inside two minutes, when Zlatan Ibrahimovic raced towards goal before passing to Javier Pastore, who only had the keeper to beat, but he sliced his shot over.
Having largely been on top during the first half, Valenciennes had their best chance at goal in the 22nd minute, but Mathieu Dossevi couldn't quite reach Rudy Mater's cross after he had gotten the better of Alex near the corner flag.
However, the champions took the lead just before the break, when Ibrahimovic threaded through Cavani in a crowded penalty area, before the Uruguayan slammed a low shot from the right into the far corner.
Pastore and Cavani both wasted opportunities to double the lead after the break, before Dossevi nearly found a late equaliser, but couldn't touch home Anthony Le Tallec's cross.
PSG move top ahead of Monaco's match with Bastia, while Valenciennes stay 19th in Ligue 1.