The Nigerian international was powerless when Landry N'Guemo's 25-metre strike took a deflection off Simon Kjaer into the net in the 27th minute.
It was the first goal Enyeama had conceded in 1,061 minutes of league action and he fell short of the French top-flight record of 1,176 minutes set by Bordeaux's Gaetan Huard in the 1992-93 season.
Bordeaux finished the game with 10 men after Maxime Poundje picked up a straight red card in the 57th minute for a rough challenge on Franck Beria.
Lille have 36 points from 17 games. Monaco, a point behind in third, host lowly AC Ajaccio later on Sunday (2000 GMT).
Leaders Paris St Germain, on 40 points, thrashed Sochaux 5-0 on Saturday.
(Reporting by Julien Pretot, editing by Justin Palmer)
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