Delaney, the Atlantic Coast Conference's leading scorer (19.8 points) and an 85-percent free throw shooter, was 20 for 23 from the line to equal the mark set by Dorenzo Hudson against Seton Hall earlier this season and Terry Penn against The Citadel in 1957. Delaney also scored at least 30 points in a game for the third time this season.
The Hokies (18-4, 5-3) made 38 of 46 foul shots, season highs in both categories. Clemson went 14 for 21 from the line.
"We win ugly games. That's our team," Delaney said. "I'm pretty sure if you look at the stats in the ACC, we're not at the top of the offensive stuff. But we're a scrappy team and we like playing. We also play good defense and we hit some free throws. Good teams win these types of games."
Both teams shot the ball poorly. The Hokies, playing less than 48 hours after beating North Carolina, missed their first 10 shots and hit only 30.6 percent for the game (15 for 49). Clemson shot a season-worst 30.6 percent, hitting 19 for 62.
"The offenses were offensive and the defenses were aggressive," Virginia Tech coach Seth Greenberg said. "I don't know how to describe it except that both teams played so hard defensively that we set offense back a couple of years."
Virginia Tech, 12-0 at home this season, trailed 37-36 with 15:40 remaining, but the Hokies went on a 15-4 run to take control of the game. Delaney and Jeff Allen each scored five points in that run and the Tigers got no closer than six the rest of the game.
Tanner Smith, Jerai Grant and David Potter each scored 11 for the Tigers (16-7, 4-5).
Trevor Booker, who came into the game averaging 15.8 points and 8.6 rebounds for Clemson, finished with seven points and four rebounds. He spent most of the game on the bench in foul trouble.
"They adjusted better to the officiating than we did," Clemson coach Oliver Purnell said. "Foul trouble has been a problem for us. I'm just very disappointed that we didn't get the job done."