PSG continued to look the more likely of the two sides, and almost opened the scoring when Lucas found Adrien Rabiot with a corner, but the youngster could not flick it in.
The deadlock was finally broken with just over an hour gone as Ibrahimovic squared the ball in for Chantome to guide past Ligali.
The home side tried to respond quickly, but Luiz was on hand to make sure that Lucas Barrios did not find Kevin Berigaud just a few yards out.
After surviving a strong spell from Montpellier, PSG put the win beyond doubt when Javier Pastore crossed the ball in from the left, leaving Ibrahimovic with a simple header from close range.
Dabo provided some faint hope for the home side in the final stages as he tried to set up a late goal, but Marco Verratti made the stop after Pastore had slipped while marking him.
Montpellier's attempts to try to get a goal back cost them though, as a counter-attack in stoppage time caught the home side short at the back, allowing Lucas to rubber-stamp the win by beating the defenders with a sprint down the right before rifling the ball home.