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ANN ARBOR, Mich. -- Michigan may not be back just yet.

The Wolverines, though, are getting much closer to where they want to be under coach Jim Harbaugh.

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 after their season-opening loss at Utah. They were 1-9 in their last 10 games against ranked opponents -- the lone victory was against Notre Dame two-plus years ago -- and had won just three of 22 games against teams in The Associated Press poll since midway through the 2009 season.

"It feels good to finally beat a ranked team," running back De'Veon Smith said. "We have to keep the momentum going and keep making statements."

Harbaugh was happy with the win, but doesn't want his team to get too excited.

"We're not getting out in front of our headlights and patting ourselves on the back," he said.

Smith ran for 125 yards on 16 carries, including a tackle-breaking, 60-yard TD, before leaving the game late in the third quarter after appearing to hurt his right ankle. After being evaluated in the locker room, Smith was wearing a walking boot as a precaution. X-rays were negative.

"I expect to play next week," he said.

Michigan opens Big Ten play at Maryland.

The Cougars (2-2) have back-to-back losses, including a one-point setback at then-No. 10 UCLA. That came after a come-from-behind win against a then-ranked Boise State and beating Nebraska on a Hail Mary.

BYU was shut out for the first time in 143 games, dating to a 3-0 loss to rival Utah in 2003, and looked overmatched from start to finish.

"That was the best team we played to this point not only physically, but execution wise," Cougars coach Bronco Mendenhall.

Michigan held a team scoreless for the first time in nearly three years.

"Our defense was playing lights out," Rudock said. "Whenever you have a shutout that makes it easier on the offense."

Indeed.

It also helps when a quarterback avoids turnovers.

Rudock threw five interceptions and lost a fumble in his first three games for Michigan after graduating and transferring from Iowa. Against BYU, he didn't appear to make many mistakes.

Rudock was 14 of 25 yards for 194 yards and a TD. He ran for 3- and 17-yard scores on plays that were designed for passes. Instead of forcing passes, he threw the ball away or ran it himself and his coach noticed.

"There must've been four or five throwaways," Harbaugh said.

Rudock threw a 4-yard TD to Amara Darboh to put the Wolverines up 14-0 early in the second. The wide receiver made a one-handed, leaping, twisting catch earlier in the game that wasn't even the highlight of his week. Darboh, who is from Sierra Leone, became a U.S. citizen on Thursday. The achievement was celebrated by his team the previous night with hamburgers, cake, balloon and "USA!" chants that surprised Darboh.

"It was more than I expected," he said.

Smith added to Michigan's highlight reel, running into the middle of the line and looking 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.

"I thought I was down for a second," Smith said. "Once I got to the second level, I was not going to let No. 15 tackle me."

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 at the Big House.

"They outmanned us, outplayed us, outperformed us," Mangum said. "They just, you know, took it to us."