This time, it was Michigan’s turn to miss.

Nolan Smith scored 24 points and the top-seeded Blue Devils held their breath as the Wolverines’ last shot clanged off the iron, sealing a 73-71 win yesterday that marked the 900th victory of coach Mike Krzyzewski’s Hall of Fame career.

“The 900, it means that we’re advancing,’’ Krzyzewski said. “That’s the main thing.’’

Kyle Singler added 13 points for the Blue Devils (32-4), who shot 51 percent, never trailed in the second half, and advanced to the Sweet 16 for the 12th time in 14 years. Next stop: Anaheim, Calif., for the West Regional semifinals Thursday night.

Parts of this game felt awfully familiar for Duke, which capped its run to the national championship last year with a dramatic 2-point victory over Butler that wasn’t settled until Gordon Hayward’s halfcourt heave ricocheted off the glass and the iron at the buzzer.

“We told our kids it would be like playing Butler in the national championship — a very similar, tough-minded, really, really good basketball team,’’ Krzyzewski said.

“I’m proud of our effort and obviously ecstatic that we’re moving on.’’

One key difference: The eighth-seeded Wolverines (21-14) gave themselves a much cleaner look on their final shot.

Michigan, which trailed by 15 with 10:51 to play, clawed within 1 point twice in the final 90 seconds before Smith missed a free throw with 8.7 seconds left to give the Wolverines one last chance.

Darius Morris zipped downcourt and put up a runner in the lane with two seconds left, but the shot bounced off the back iron and the rebound went to Smith at the buzzer.

Morris finished with 16 points to lead Michigan, which made seven 3-pointers — the most allowed by Duke in a month.

Kyrie Irving and Ryan Kelly scored 11 points apiece for the Blue Devils, who won their eighth straight game in the NCAA Tournament.

“I don’t want to take this Duke jersey off. As simple as that,’’ Smith said. “Every game could be my last.’’

Krzyzewski improved to 900-283 in his 36th season and can catch his mentor and college coach for first on the career list next weekend. He would match Bob Knight with a victory in the regional final, and would pass him with one win in Houston that also would put the Blue Devils back in the title game.

“There will be a lot of guys who will win 900 games eventually, but to be the first two and for it to be a coach and his player to do it, it’s something very unique,’’ Krzyzewski said.

Still, Michigan nearly made Coach K wait until next year — or at least work overtime — to try for No. 900.

Coach John Beilein frustrated Duke by mixing his defenses, and Tim Hardaway Jr. reeled off 7 consecutive points down the stretch, capped by a 3-pointer that made it 70-69 with 1:27 remaining.

“That’s all we needed to do was make a shot,’’ Beilein said.

Duke milked the clock before Irving’s banked-in jumper with 32 seconds left, but Morris followed with a layup that cut it to 72-71 with 10 seconds to go.

Michigan fouled Smith with 8.7 seconds left, and he made his first attempt, but missed the second. Zack Novak got the rebound and got it to Morris, who headed straight for the lane and put up Michigan’s last shot.

After the horn sounded, Morris lay face down on the floor and repeatedly slapped the court with his palm in frustration.

“Darius got a great shot off, [a] shot he hits a lot in practice,’’ teammate Stu Douglass said. “When it was in the air, I thought it was going down.’’

Hardaway scored 15 points, Evan Smotrycz had 13, Novak scored 12, and Jordan Morgan finished with 10 for the Wolverines, who don’t have a senior on the roster. They were denied their first trip to the round of 16 since 1994.

This was the first postseason meeting between the big-name schools since the 1992 national championship game, won by Christian Laettner and the Blue Devils over the Wolverines and the Fab Five.