The Bruins (10-3) outscored the Hokies (8-5) 28-5 in the second half.
Hundley had an 86-yard touchdown run and finished with 161 yards on 10 carries, and completed 16 of 29 passes for 226 yards. He was selected the co-MVP along with linebacker Jordan Zumwalt, who had 10 tackles and an interception.
After Virginia Tech cut it to 14-10 on Michael Branthover's 22-yard field goal with 3:53 left in the third quarter, UCLA answered with a 12-play, 85-yard drive, capped by Paul Perkins's 5-yard run early in the fourth.
Hokies backup quarterback Mark Leal then threw a pass under heavy pressure that linebacker Myles Jack intercepted and returned 29 yards for a touchdown that made it 28-10.
Virginia Tech, which lost starting quarterback Logan Thomas to an injury in the second quarter, got its final points when UCLA punter Sean Covington stepped on the end line for a safety with 9:38 left.
UCLA pushed it to 35-12 on Hundley's 8-yard touchdown pass to Thomas Duarte with 7:31 to play. The Bruins stayed aggressive late, and Hundley fired a 59-yard scoring strike down the right sideline to Shaquelle Evans for another score with 5:49 remaining.
UCLA led 14-7 after the first half. Hundley had six carries for 168 yards in the half. He set the Sun Bowl record for rushing yards by a quarterback by halftime.
Worse for Virginia Tech, which entered the game ranked No. 4 in the nation in total defense, was that the Bruins rushed for 202 yards in the first half. That already was the most rushing yards the Hokies had given up in a game this season. UCLA finished with 250 yards.
The Bruins struck first on Hundley's 7-yard TD run in the first quarter. That capped a six-play, 74-yard drive that opened the game.
After an exchange of punts, Virginia Tech answered with J.C. Coleman's 1-yard scoring dive midway through the quarter.John Erfort, Associated Press