The win makes the Utes (6-4, 3-4 Pac-12) bowl-eligible for the ninth straight year and gave offensive coordinator Norm Chow another victory against a former team.
With wintry conditions at the start of the game, the Utes became even more one-dimensional behind the diminutive White. He didn't disappoint, vaulting from 10th on Utah's single-season rushing chart all the way to No. 4 with 1,191 yards - passing Eddie Johnson, Eddie Wide, Keith Williams, Quinton Ganther and Del Rodgers.
UCLA (5-5, 4-3) saw its grip on a possible Pac-12 South title slip away with two Kevin Prince interceptions. The Bruins will need a win at home against Colorado or at USC to qualify for a bowl for the 10th time in the last 12 seasons.
The win was Utah's third straight. Utah's defense, ranked No. 3 overall in the Pac-12, held the Bruins to a pair of Tyler Gonzalez field goals. It intercepted Prince twice, with Black taking the second one back for the TD.
Black was the hero a week ago when he made an end-zone interception in a win over Arizona.
White's 1-yard touchdown run gave Utah a 7-3 lead with 5:34 left in the second quarter. The junior running back accounted for all 39 yards on the scoring drive with seven carries.
Utah quarterback Jon Hays was just 2 for 7 for 5 yards passing in the first half, but was 3 for 3 on the opening drive of the second half. He passed 16 yards to Devonte Christopher on third-and-5, then hit Dres Anderson for 33 yards over the middle on the next play. He capped the drive with a 13-yard TD pass to White, who had beaten linebacker Sean Westgate in the corner of the end zone, for a 14-3 Utah lead.
White scored on a 22-yard run to give Utah a 21-3 lead with 3:18 remaining in the third quarter.
UCLA cut the gap to 21-6 on Gonzalez's 35-yard field goal early in the fourth, but Black's interception return sent the Bruins limping home.
It was a shocking turnaround for the Bruins, who entered on a two-game winning streak and feeling pretty good about themselves.
Ninety minutes before kickoff, a pair of UCLA offensive linemen could be found playing shirtless in the snow, tossing wobbly passes around like school kids. Not to be outdone, up to a dozen Utah players began warming bare-chested a few minutes later, large flakes falling all around them and starting to stick.
A UCLA sports information official said the Bruins hadn't played a ''snow game'' in at least 31 years. There were flurries in the EagleBank Bowl in Washington, D.C., in December 2009 when the Bruins rallied from a two-touchdown deficit to beat Temple 30-21.
But an icy field and wind chill that made it feel like 19 degrees at kickoff were more the issue in that game, which saw the Bruins change game plans at halftime and run plays that required little or no change of direction.
That win gave the Bruins a winning season under coach Rick Neuheisel. This game ended much differently.