Sherwood Brown scored 24 points and Bernard Thompson had 23 to lead Florida Gulf Coast, the champions of the Atlantic Sun Conference
FGCU (25-10) will play 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 fourth-seeded New Mexico, one of its youngest FGCU's first student was admitted in 1997 got one that was even bigger.
The Eagles' big run gave them a 52-33 lead with 12:28 to play. The Hoyas staged a furious rally to get within 72-68 with 52 seconds left but the Eagles went 6 of 10 from the free throw line to seal it.
"In the second half, we pushed the ball, we got out, we ran, we made shots, got some alley-oop dunks to energize the crowd. I'm very proud of our players," said coach Andy Enfield, whose wife supermodel Amanda Marcum was shown several times on the arena's big screen.
For those who don't know FCGU, and that was probably plenty of people as of Friday afternoon, Florida Gulf Coast is a state university in Fort Myers with an enrollment of about 12,000 students.
This is FGCU's first tournament and Georgetown's 29th, including the 1984 national championship. But the Eagles did beat Miami earlier this season.
It was another disappointing NCAA exit for the Hoyas (25-7), who have lost to a double-digit seed in their last four appearances. The last time they made it to the second weekend of the tournament was in 2007, when they reached the Final Four.
Markel Starks had 23 points for the Hoyas, a tri-champion of the Big East regular season and one of the top defensive teams in the nation.
That didn't seem to bother the Eagles much.
While Georgetown came in allowing 55.7 points per game, FGCU beat that number with 9:22 to play when it led 57-40. The Hoyas allowed opponents to shoot 37.6 percent from the field, fourth-best in the country. The Eagles shot 42.9 percent (21 of 49) and they held the Hoyas to 37.5 percent from the field (24 of 64).
The FGCU fans who made the trip to Philadelphia were loud all game. The rest of the crowd at Wells Fargo Center joined them during the big run and there's nothing to bring fans together like rooting against a heavy favorite.
The Eagles charged at their fans when the game ended and after some of them shook hands with Hall of Famer and TV analyst Reggie Miller it was a celebration that could be felt all the way to back to campus.
Big East Player of the Year Otto Porter Jr. had 13 points on 5-of-17 shooting and 11 rebounds. On this night he couldn't match Brown, the A-Sun's player of the year.
"It feels really good to be in this position right now," Brown said after the game.
The Hoyas used an 8-0 run to take an 18-11 lead midway through the first half but that's where their offense went cold very cold.
The Eagles closed the half on a 13-4 run as Georgetown missed nine straight shots and committed five turnovers. FGCU took a 24-22 lead on two free throws by Eddie Murray with 26 seconds left. In another example of how Georgetown was out of synch offensively, the Hoyas passed the ball around as the halftime horn sounded, giving the Eagles the two-point lead after their first half of an NCAA tournament game.
As the night wound down, one fan yelled at the Eagles to stick around Philly a couple of more days.
"Get a cheese steak, kid! Get a cheese steak!"
The crowd then paid Florida Gulf Coast the ultimate tribute: the E-A-G-L-E-S! Eagles! chant reserved for their favorite NFL team.