The Uruguay striker put PSG ahead after six minutes with a fine volley following a long pass from Marquinhos and Argentine Angel di Maria doubled the lead with a cool finish four minutes before halftime.
Cavani, the leading scorer in Ligue 1 this season, turned in Di Maria's cross to grab his second two minutes after the interval for his 25th of the campaign.
PSG, bidding for their fifth league title in a row, trail Monaco on goal difference, on 55 points, three ahead of third-placed Nice heading into their home Champions League last-16 first-leg match against Barcelona on Tuesday.
Monaco host Metz on Saturday. Bordeaux stayed seventh in the standings on 36 points.
(Reporting by Ed Osmond, editing by Ken Ferris)
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