HOUSTON >> Blake Corum ran for 134 yards and two fourth-quarter touchdowns as Jim Harbaugh and No. 1 Michigan — undeterred by suspensions and a sign-stealing case that shadowed the program — completed a three-year climb to a national championship by beating No. 2 Washington 34-13 Monday night in the College Football Playoff title game.

The Wolverines (15-0) sealed their first national title since 1997 when Corum, who scored the winning touchdown in overtime to beat Alabama in the Rose Bowl semifinal, blasted in from the 1-yard line with 3:37 left to put Michigan up by 21 and set off another rousing rendition of “The Victors.”

After nine seasons coaching his alma mater and in his third consecutive playoff appearance, Harbaugh delivered the title so many expected when he took over a struggling powerhouse in 2015 — despite missing six regular-season games this season while serving separate suspensions.

And he did it with a team his old coach, Bo Schembechler, would have adored. The Wolverines ran for 303 yards against Washington (14-1), and their defense held Michael Penix Jr. and the Huskies’ prolific passing game to just one touchdown while intercepting the Heisman Trophy runner-up twice.

Penix’s remarkable six-year college career ended with maybe his worst performance of the season. Usually unfazed by pressure, Penix was not nearly as precise against a Michigan defense that took away his signature deep throws.

Penix finished 27 for 51 for 255 yards and a touchdown.

Michigan’s J.J. McCarthy had a modest game, throwing for 140 yards and running for 31. But it was enough for him to improve to 27-1 as a starter for the Wolverines.

Michigan gave Washington a taste of life in the Big Ten, where the Pac-12 champions are heading next season, and the Huskies were up for the grind for a while.

Two long touchdown runs by Donovan Edwards and 229 yards rushing in the first quarter put the Wolverines up 17-3 early in the second and conjured up memories of last year’s historic Georgia blowout of TCU.

Washington stabilized and didn’t allow the Wolverines another point in the first half. After the Huskies stopped Michigan on a fourth-and-2 from the UW 38 with 4:46 left in the second quarter, Penix went to work.

He found Jalen McMillan on a fourth-and-goal with 42 seconds left for a 3-yard touchdown. After being on the verge of getting buried by the Wolverines, the Huskies fans sang along to “Who Let the Dogs Out,” happily down 17-10 at half.

Will Johnson’s interception of Penix on the first play of the second half gave Michigan another opportunity to open up a two-touchdown lead, but the Huskies forced another field goal by James Turner to make it 20-10.

Michigan nursed a touchdown lead until halfway through the fourth quarter, when it put together 71-yard drive, capped by Corum’s tackle-breaking 12-yard touchdown that finally gave the Wolverines some room with a 27-13 lead and 7:09 left.

Corum, the engine of ground-and-pound offense and heart and soul of team loaded with fourth-, fifth- and even sixth-year players, missed the CFP last year with a knee injury. He was named offensive player of the national title game.

“Michigan, this is for you,” Corum told the Wolverines fans.