Uruguay striker Cavani opened the scoring with his 31st league goal of the season in the first half and Argentine winger added another after the break to put PSG on 80 points from 34 games.
They lead Monaco by three points but the principality side, who face a tricky trip to Olympique Lyonnais on Sunday, have two games in hand.
The defeat left Montpellier in 12th place on 39 points, eight points above the relegation zone.
Ligue 1 top scorer Cavani put the hosts ahead on 29 minutes when he latched on to Blaise Matuidi's cross for his 44th goal in all club competitions this season.
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Montpellier had a chance to equalise two minutes later but Ellyes Skhiri's header crashed on to Kevin Trapp's bar.
Javier Pastore dictated play in midfield in delicate fashion as PSG dominated and they doubled their tally three minutes into the second half with a superb curled shot.
Unai Emery's side then played safely to secure their eighth league win in a row.
(Reporting by Julien Pretot; Editing by Clare Fallon)
