Leading scorer Erick Green struggled to 10 points on 3-of-11 shooting for the Hokies (12-10, 2-6 ACC), who snapped a three-game slide and stayed out of last place in the conference.
Virginia Tech scored first and never trailed, building up a 42-28 lead at the half as Eddie poured in 13 points before the break.
The Hokies still led, 64-50, after Finney-Smith drained a 3-pointer with 5:57 to play. That’s when the Tigers began to make it interesting, scoring seven straight points to cut the deficit to 64-57 with 3:28 on the clock.
After a Virginia Tech basket, K.J. McDaniels went to work, converting a layup and two straight dunks to make it 66-63.
Finney-Smith’s 3-pointer would be the Hokies’ last field goal but Clemson could not take full advantage. McDaniels had a chance to tie it but missed two free throws with three seconds left.
McDaniels finished with 14 points and Devin Booker added 11 points and 11 rebounds for the Tigers (11-11, 3-5), who have dropped two in a row and five of seven.