Bordeaux's Samuel Kalu cancelled out Karl Toko-Ekambi's first-half opener before Dubois pounced two minutes into added time to put Lyon on 46 points from 22 games, one ahead of Paris Saint-Germain and Lille who play on Sunday.
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The result left Bordeaux in seventh place on 32 points.
"We have a goal: qualify for the Champions League again," said Dubois. "Lille and PSG have a game in hand so in terms of points per game we're behind. But we're staying focused on our objectives."
At the Groupama stadium, Toko-Ekambi scored his 10th league goal of the season when he latched onto Memphis Depay's cross.
Lyon had won all 10 games in which they opened the scoring this season but Bordeaux had other ideas as they struck back 10 minutes into the second half with Kalu netting from close range after benefiting from the home side's slack defending.
Lyon grabbed the points when Dubois' strike flew into the top corner, giving Rudi Garcia's side a second win in a row.