Tom Ramsey rallied the No. 12 Bruins from a 21-point deficit by passing for two touchdowns and running for another at Ann Arbor, Mich.
"Michigan dominated the line of scrimmage defensively," UCLA Coach Terry Donahue said. "Being down 21-0 early in the game, we decided to let Ramsey play loose."
Dokie Williams' 65-yard kickoff return set up tailback Kevin Nelson's two-yard sweep around left end, with 2:50 left in the third quarter. That gave the Bruins (3-0) their first lead, 28-27.
John Lee kicked a 26-yard field goal with 11:46 left to make it 31-27, but UCLA lost a fumbled pitchout on the Michigan 48 with 65 seconds left.
Steve Smith, intercepted three times that half, passed 15 and 17 yards to Anthony Carter to get to the UCLA nine, but his third-down pass to the well-covered Carter was overthrown and No. 20 Michigan (1-2) lost its second straight in a season for only the third time since Bo Schembechler became coach in 1969.
Carter set a Big Ten record with his 30th touchdown catch, on a five-yard pass from Smith in the first half after the Wolverines took over on UCLA's seven on a poor punt off a bad snap. Carter caught eight passes for 123 yards despite playing with a slight groin muscle pull.
Ramsey's first pass of the game, a deep throw for split end Cormac Carney from his 20, was picked off by Evan Cooper and turned into a nine-yard touchdown by tailback Larry Ricks.
Michigan got two more touchdowns before Ramsey's 46-yard sideline pass to Williams, on third down, cut the deficit to 21-7. Two minutes later, he ran in from the one to make it 21-14.
Bruins safety Don Rogers intercepted Smith at the start of the second half, setting up Ramsey's six-yard scoring pass to wide receiver JoJo Townsell. That made it 24-21 and the Wolverines were held to three points that half, on a 48-yard field goal by Ali Haji-Sheikh that was the longest of his career and the 22nd he has kicked, making him Michigan's all-time field goal leader.
Ramsey threw 36 times, completing 22 for 311 yards with one interception.