McClinton led Miami with 23 points while making six 3-pointers.
McClinton's last 3-pointer gave Miami a 63-60 lead. He made one of two free throws with 30 seconds left to push the lead to 64-60.
Georgia Tech had four misses before Matt Causey, who scored 20 points, hit a 3-pointer with 1.9 seconds left. Causey was guarded closely by Lance Hurdle on the shot, but Hurdle was not called for a foul.
Miami (17-7 overall, 4-6 in the Atlantic Coast Conference) completed a sweep of the two regular-season games with Georgia Tech (11-13, 4-6).
Georgia Tech fell to 4-6 at home, including a 1-4 mark in ACC games at Alexander Memorial Coliseum.
James Dews had 11 points for Miami. Jeremis Smith had 11 for Georgia Tech.
McClinton's fifth 3-pointer tied the game at 57-57 with 2:16 left, but Anthony Morrow answered with a 3 for Georgia Tech. Miami pulled even again at 60-60 on Anthony King's three-point play with 1:27 left.
Causey scored eight straight points, including two 3-pointers, in the first five minutes to give Georgia Tech a 10-5 lead, but the Yellow Jackets were hurt by 15 turnovers in the half.
Miami led 27-26 at the break on McClinton's first 3-pointer after four misses.
Causey remained in the Georgia Tech lockerroom for the start of the second half. A Georgia Tech spokesman said Causey was hyperventilating. The senior returned to the bench less than three minutes into the second half and entered the game at the 15:48 mark.