The success moved PSG eight points clear of second-placed Monaco ahead of the weekend's matches, while Valenciennes remain in the thick of a relegation battle.
The hosts started strongly, Yohan Cabaye's free-kick picking out Ibrahimovic, who flicked the ball on to Lavezzi, but the Argentinian's backheel was blocked by goalkeeper Nicolas Penneteau.
Lavezzi found the net after only 18 minutes, though, helping the ball home from close range after Ibrahimovic's free-kick fell kindly for him.
PSG's front two were causing the visitors all sorts of problems and Ibrahimovic set up another chance for his team-mate, whose shot from inside the area was saved by Penneteau.
The Valenciennes keeper was keeping his side in the game and he did well to keep out a low Ibrahimovic drive.
But the Swede doubled his team's lead six minutes into the second half, volleying home right-footed from point-blank range following a cross from Cabaye.
And the hosts had victory secure two minutes later as the unfortunate Kagelmacher turned a cross from the impressive Lavezzi into his own net.
VA at least showed some fight, Tongo Doumbia bringing a smart stop out of Salvatore Sirigu just after the hour mark, but PSG were already home and dry.