The Eagles, in their second season of being eligible for Division I postseason, became just the seventh No. 15 seed to beat a No. 2.
FGCU (25-10) plays the winner of the game between seventh-seeded San Diego State and No. 10 Oklahoma in the third round on Sunday.
A night after America's oldest university, Harvard, pulled off a major upset over third-seeded New Mexico, one of its youngest -- FGCU's first student was admitted in 1997 -- got one that was even bigger.
The Eagles took control with a 21-2 run that gave them a 52-33 lead with 12:28 to play, though the Hoyas used a furious rally to get within 72-68 with 52 seconds left.
It was another disappointing NCAA exit for the Hoyas (25-7), who have lost to a double-digit seed in their past four appearances.
Markel Starks scored 23 points for the Hoyas.
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