Miami, the 10th seed and defending tournament champ, won for the first time in three tries against Virginia Tech this season.
Rion Brown led the Hurricanes (17-15) with 15 points, but shot 3 of 13 from the floor.
Miami was up 49-42 just past the midway point of the second half, but Virginia Tech surged ahead behind a 10-2 run. The Hurricanes regained the lead at 53-52 on a Swoope jumper with 2:42 remaining.
Still clinging to the narrow lead, Miami committed a turnover on an inbounds pass inside the final minute.
Joey Van Zegeren was fouled on a shot attempt from the paint and had a chance to put the 15th-seeded Hokies on top. However, he missed both free throws with 9.5 seconds left.
Brown then went to the foul line and converted both to make it 55-52.
Manu Lecomte then fouled Virginia Tech's Devin Wilson, sending him to the line for a one-and-one. He sank the first attempt before missing the second. Jarell Eddie grabbed the offensive rebound, but lost control of the ball as he was going up from the base line for a potential game-tying shot.
Swoope then made two free throws as Miami advanced to play seventh-seeded North Carolina State in the second round on Thursday.
Eddie was the lone Virginia Tech (9-22) player to reach double figures in points, finishing with 16.
The Hokies' two wins over Miami were their only ones in conference play.