Oduya skated into the right circle on a break and fired a slap shot that beat Jhonas Enroth high to the glove side, allowing the Jets to stop a two-game losing streak.
Enroth played well, making 39 saves, but was saddled with the loss for the Sabres, who fell for the sixth time in 10 games.
Tyler Myers got Buffalo's only goal.
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