Baylor advanced to the quarterfinals and will play host to Auburn on Tuesday night. The Bears, who have won five of their past six games, including three in the Big 12 tournament and two in the NIT, improved to 22-14.
The only other time the Bears have won two postseason games in a season was in 1948, when the Bears lost to Kentucky in the NCAA tournament championship game.
"We have a senior-laden group and they provide great leadership," Baylor coach Scott Drew said. "They've been playing well and they want to keep playing. They did a great job of following the game plan and did a great job of making sure we didn't get rattled at the end."
Malcolm Delaney led Virginia Tech (19-15) with 14 points.
The Bears never trailed, taking a 22-5 lead in the first 12 minutes in part because the Hokies made just one of their first 17 attempts.
Baylor, which shot 67 percent in the first 20 minutes, got 12 points from 7-foot center Josh Lomers, who came into the game having scored in double figures just twice all season.
The Bears pushed the lead to as many as 28 in the second half.
An 18-3 run, capped by two free throws from A.D. Vassallo, got the Hokies to within 65-52.
After a dunk by Rogers, Delaney hit a 3-pointer cut the lead to 12 with 4:57 remaining. But Jerrells hit two free throws and Henry Dugat drained a 3-pointer from the corner on back-to-back possessions to push the lead to 17, and the Bears were not threatened again.
They shot 61.7 percent for the game, the best against the Hokies this season.
"Our inability to make a shot early really affected our ability to defend," Virginia Tech coach Seth Greenberg said. "We just stopped checking people. The basket got big for them and they just physically overpowered us up front. We have to get stops to be successful, so that?s disappointing."