The Tigers (11-8, 3-4 Atlantic Coast Conference) had let a double-digit lead slip away and trailed 59-58 when Jennings took over. His foul shot with 3:20 remaining gave Clemson the lead for good at 61-60.
Jennings, a senior, also tied his career best with 14 rebounds and provided the push for Clemson when leading scorer
Harrison, a transfer from BYU, also had his career high for Clemson with 19 points.
Jennings also posted career-best showings with four blocked shots and by going 16 of 18 from the foul line.
Clemson came into this one off two close defeats, 66-62 at 14th-ranked North Carolina State last Sunday and then 60-57 at Florida State this past Thursday night when Michael Snaer banked home a 3-pointer at the buzzer for the game-winner.
Virginia Tech had lost its two-game ACC win streak earlier this week when it fell to rival Virginia. And it looked like the Hokies might be on the way to two straight losses when Clemson broke out to a 12-0 lead less than seven minutes into the game.
McDaniels had two of his three first-half 3-pointers during the Tigers' surge while Virginia Tech missed its first 10 shots. But like always when these teams play -- 12 of the 13 meetings since the Hokies joined the ACC have been decided by single digits -- things tighten up.
Virginia Tech found lanes in Clemson's usually stout defense -- the Tigers are second in the ACC in points given up -- and rallied from the foul line as it made 12 of 15 free throws in the opening half.
Green's two foul shots tied the game at 31. Green's driving layup a minute later sent the game to the locker room tied at 33. Green had 14 points for the Hokies.
McDaniel led the Tigers with nine first-half points, but played just nine minutes because of foul problems.
The game got physical in the second half with Jennings getting called for a flagrant foul and Tigers coach
Virginia Tech's Johnson was back at Clemson for the first time since he spent less than two weeks as a Tigers assistant last spring. He was hired by Brownell to replace Rick Ray, who took the head coaching job at Mississippi State. But then Virginia Tech let Seth Greenberg go and called on Johnson to take over.