Gardner's clutch free throws with 8.3 seconds remaining put Marquette (11-3, 2-0 Big East) up by three points at 49-46.
The Hoyas had a chance to tie the score when Golden Eagles' Trent Lockett fouled Georgetown's Greg Whittington on a 3-point try, giving him three free throws. Whittington drained the first two shots but, after a Marquette time-out, missed the third.
Lockett (nine points, 10 rebounds) then grabbed the defensive carom to assure the victory.
Marcel Starks put in 18 points and dished off seven assists to lead the Hoyas (10-2, 0-1).