Damarcus Harrison had 12 points for the sixth-seeded Tigers (20-11), who will face third-seeded Duke on Friday. Rod Hall added 10 points and Jaron Blossomgame cleared nine boards.
Trae Golden finished with 23 points for the 11th-seeded Yellow Jackets (16-17). Robert Carter Jr. tallied 13 points and nine rebounds while Kammeon Holsey chipped in 10 points.
Georgia Tech shot 33.3 percent from the field in the first half as it led 29-27 at the break. Clemson made 42.3 percent of field goal attempts but took seven less shots.
The Tigers struggled from the floor in the second frame (.292), but were 12- of-14 at the free-throw line. After going down seven over halfway through the stanza, Clemson went on a 9-2 run to tie the game up at 51-51. With one second left in regulation, Georgia Tech's Daniel Miller connected on a shot to tie the game at 55-55 and send the game to overtime.
Clemson closed out the extra period on an 8-3 run to secure the win.
The Tigers shot an impressive 86.2 percent at the charity stripe on 29 attempts, while Georgia Tech was a mere 11-of-20 at the stripe.