The Uruguayan frontman struck at the end of the first half to ensure Laurent Blanc's men returned to winning ways after Sunday's draw with Ligue 1 title rivals Monaco
The champions headed into Wednesday's Ligue 1 clash on the back of Sunday's 1-1 draw with early pacesetters Monaco and produced a largely underwhelming performance at the Stade du Hainaut.
However, Cavani proved to be the difference between Laurent Blanc's side and their struggling hosts, as he netted in first-half injury-time to secure all three points for PSG.
Valenciennes made three changes from the side beaten 4-0 by Nice last time out, Gary Kagelmacher replacing Benjamin Angoua in the centre of defence, while David Ducourtioux was chosen ahead of Jose Saez in midfield and Mathieu Dossevi stepped in for Gregory Pujol in the attacking three.
Blanc also opted to shuffle his pack, with Alex coming in for injured captain Thiago Silva and Christophe Jallet and Lucas Digne taking the two full-back spots in place of Gregory van der Wiel and Maxwell respectively.
Javier Pastore also returned instead of Thiago Motta in midfield, and it was the Argentinian who created the game's first chance as he surged through the home defence in the third minute before blazing over the bar from a tight angle after playing a neat one-two with Zlatan Ibrahimovic.
But despite that early opportunity, PSG struggled to impose themselves, with Daniel Sanchez's hosts doing most of the pressing as they looked to end a run of five consecutive Ligue 1 defeats.
Chances were few and far between in a dour first half that lacked any real tempo, although Marquinhos did come close to scoring his second goal for Blanc’s side as he headed wide seven minutes before the interval.
Valenciennes were dealt a blow in the closing stages of the first half when experienced defender Rudy Mater was forced off with an injury, to be replaced by Saliou Ciss.
And they then found themselves a goal down just before the break, Cavani slotting a neat finish into the bottom corner in added time after being played in by a deft pass from Ibrahimovic.
PSG made one change at half-time, Zoumana Camara coming on for Alex, and they had Marco Verratti to thank for preserving their advantage just a minute into the second period as the Italian midfielder cleared Lindsay Rose's header off the line.
Valenciennes continued to do most of the pressing in the second period, but their forays forward provided no reward with PSG remaining dangerous on the counter.
Sanchez's men looked to tire as the contest entered the closing stages, Ibrahimovic twice going close for PSG in their quest to kill the match off.
Anthony Le Tallec fired wide of the post with a curling free-kick seven minutes from time for the hosts, but they were not able to claim a point and fell to their sixth straight loss.