The Gators (3-1) held a 36-32 lead at the half behind 10 points from Matt Bonner, but went cold over the final 20 minutes, hitting just 9-of-24 shots in the second half.
With the Gators trailing 67-65 in the waning seconds, Anthony Roberson missed a short jumper that would have tied the game. After Stanford's Justin Davis pulled down the loose ball, Roberson quickly fouled him and Davis hit two shots to ice the game.
The Gators shot under 50 percent from the floor for the first time this season, hitting just 39.3 percent. Bonner led the way for the Gators with a season-high 19 points, while Matt Walsh chipped in with 17 points and six assists.
Stanford (4-0) had four players in double figures, led by Little with 18 points. Davis added 14, while Matt Lottich scored 13 and hit a trio of three-pointers.
The loss was the first for the Gators in NIT play, as they entered the game with a perfect 6-0 record all-time in the tournament after sweeping the 1987 title.
The Gators will now face Kansas for the first time since 1996, the year before current head coach Billy Donovan's arrival. The Gators are 0-2 all-time against the Jayhawks.
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