The Cavaliers (8-5, 2-1) now have a three-game winning streak against Syracuse (7-6, 1-1).
Buddy Boeheim's 3-pointer with 1:19 left brought Syracuse within 72-69, but the Orange missed their last three shots while Clark made two free throws with 22 seconds left to seal it.
Jimmy Boheim's layup to start the second half gave Syracuse its only lead of the game at 35-33. Clark made a layup 24 seconds later, Franklin buried a 3-pointer with 18:24 remaining and Virginia led for the remainder.
Clark finished 6-for-9 shooting, including 3 for 5 from 3-point range, distributed eight assists and grabbed four rebounds. Jayden Gardner scored 15 and Shedrick scored 12 with 11 rebounds.
Buddy Boeheim scored 27 points and Jimmy Boeheim 17 for Syracuse. The Orange shot 36.7% overall, including 10 for 30 from 3.
UVA entered the game holding the opposition to 49.6 points per game, 33.1% field goal shooting and 25% from 3-point range in its victories
Virginia built a quick 10-3 lead at the outset before the Orange closed to 17-13. The Cavaliers responded with an 8-0 outburst in a 2:30 span before Syracuse went on to outscore Virginia 20-8 in the final seven minutes of the first half to forge a tie at 33.
UVA held Syracuse to 34 points in its last visit to Carrier Dome on Nov. 6, 2019, marking an all-time low for the Orange in a game at the Carrier Dome.