The Nigerian striker headed the winner 10 minutes from time to put Montpellier on 53 points from 25 matches, two ahead of Paris St Germain, who visit Olympique Lyon later on Saturday (2000 GMT).
Both teams created several clear chances but Montpellier finally made the breakthrough when Utaka scored from a Marco Estrada corner as the hosts piled on the pressure.
Bordeaux, who were unbeaten in Ligue 1 this year, came close in the first half when their Poland forward Ludovic Obraniak curled a shot against the post just before the break.
St Etienne stayed fourth on 43 points following a 0-0 draw at second bottom AJ Auxerre who moved up one place.
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