Marcus Georges-Hunt had 18 points for the 11th-seeded Yellow Jackets (16-16), who will face sixth-seed Clemson on Thursday. Trae Golden finished with 14 points and six assists, while Kammeon Holsey added 12 points.
Patrick Heckmann scored 21 points for the 14th-seeded Eagles (8-24). Olivier Hanlan chipped in 16 points and Ryan Anderson tallied a double-double with 15 and 12 boards.
Georgia Tech shot 40 percent on field goal tries in the first half as it led 29-25 at the break. Boston College made just 32 percent from the floor in the period.
The Eagles improved in the second frame as they drained 55 percent of their field goal attempts and went 13-of-16 from the free-throw line. After being down 10 with 4:21 left Boston College went on a 10-0 run to tie it up at 61-61 with 52 seconds. The two teams then traded free-throws and the game went to overtime.
Georgia Tech was down one with 1:44 remaining in the extra frame and went on a 7-3 run to close out the game and seal the win.
The Yellow Jackets held a 41-30 rebounding advantage over Boston College.