Garland's lay-in past defender Reginald Buckner as time wound down handed the Explorers (24-9) their first trip to the NCAA regional semifinals since 1955.
Garland finished with 17 points and Ramon Galloway drained six 3-pointers en route to a game-high 24 points.
Tyreek Duren added 19 points for the winners, who advance to play ninth-ranked Wichita State in West Regional Thursday at Los Angeles.
Marshall Henderson led the 12th-seeded Rebels (27-9) with 21 points.
Police: Sword-wielding man demanded free tacos
N.J. man wakes up from 10-hour sleep with knife in back