Jake Rudock ran for two touchdowns and threw for another one during a first half in which Michigan did all of its scoring in a 31-0 rout against No. 22 BYU on Saturday.

The Wolverines (3-1) have won three straight under Jim Harbaugh after their season-opening loss at Utah. They were 1-9 in their last 10 games against ranked opponents, and had won just three of 22 games against teams in The Associated Press poll since midway through the 2009 season.

The Cougars (2-2) have back-to-back losses, including a one-point setback at then-No. 10 UCLA. That came after they beat then-No. 20 Boise State by double digits and Nebraska on a Hail Mary.

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De'Veon Smith ran for 125 yards on 16 carries, including a tackle-breaking, 60-yard touchdown before leaving the game late in the third quarter after appearing to hurt his right ankle.

Rudock, who avoided turnovers that plagued his first three games, was 14 of 25 yards for 125 yards and a TD. He ran for 3- and 17-yard scores on plays that were designed for a passes, helping Michigan lead 31-0 at halftime. Instead of forcing passes, he threw the ball away or ran it himself.

He threw a 4-yard TD to Amara Darboh to put the Wolverines ahead 14-0 early in the second. On their next drive, Smith ran into the middle of the line and looked like he was in a rugby scrum before emerging from the pack and using a stiff-arm and spin move to break free of defensive back Michael Davis. After being evaluated in the locker room, Smith was wearing a walking boot as a precaution.

BYU quarterback Tanner Mangum looked like a freshman for the first time this season.

Mangum was 12 of 28 for just 55 yards. Entering the game, Mangum had completed 63 percent of his passes for 664 yards with four TDs in two-plus games in place of injured teammate Taysom Hill.

The Cougars averaged 310 yards passing and 122 yards rushing against three notable opponents entering the game and were held to fewer than 100 yards until the final minute.

Former New York Yankees great Derek Jeter, who attended the University of Michigan briefly and went to high school in Kalamazoo, Mich., was at the game and was given a blue jersey with No. 2 and Jeter in maize by Harbaugh before kickoff.