Lamb's 3-pointer with 3:19 remaining put the Wildcats ahead for good at 64-63 as Kentucky (25-1, 11-0 SEC) scored the game's final eight points to remain unbeaten in conference play.
The Commodores (17-8, 6-4) got 15 points from John Jenkins while losing for the third time in four games.
Brad Tinsley, Festus Ezeli and Jeffery Taylor each added 13 for Vanderbilt.
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