Cornet cancelled out Jimmy Briand’s early opener after the break and set up Moussa Dembele for the second as OL, who have 29 points from 20 games, moved from 12th to fifth.
Montpellier claimed their first away win of the season by beating Amiens 2-1 as they climbed to fifth on 30 points thanks to Andy Delort's late winner.
Bordeaux, who had not lost in the last 33 league games in which they had opened the scoring, stayed 13th on 26 points.
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Briand intercepted a poor back pass from Joachim Andersen to beat keeper Anthony Lopes from close range in the 15th minute.
Cornet, however, levelled five minutes into the second half with a slightly-deflected 20-metre strike.
Mexer et Maxwel Cornet
Image credit: Getty Images
Dembele gave the hosts the lead three minutes later with a low cross-shot after being played through by Cornet.
It was the first time Rudi Garcia’s team had won two league matches in a row since he took over in October.
Leaders Paris St Germain, who have 45 points from 18 games, host AS Monaco on Sunday.
They lead second-placed Olympique de Marseille, who have two games in hand after beating Rennes 1-0 away on Friday, by four points.
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