ANN ARBOR, Mich. -- After barely escaping with an overtime win over Michigan, Kansas coach Bill Self is a little hesitant to compare this year's Jayhawks with his national championship team from three seasons ago.

"That wasn't a good team, that was a great team," Self said. "I think that this team that we have is a good team with a chance to become really good. ... I've also got to be careful of comparing to that team. It's not fair to these guys."

The Jayhawks will welcome the comparison if they go on to win the national title, but for now, they'll have to settle for the school's best start since that 2007-08 season. Marcus Morris scored 22 points, and third-ranked Kansas outlasted Michigan 67-60 on Sunday to improve to 15-0.

The Jayhawks overcame a dreadful shooting day. They finished at 36 percent from the field and 4 of 24 from 3-point range.

Michigan (11-5) was even worse at 33 percent from the field and 4 of 28 from long distance, but the Wolverines fought back from a 13-point second-half deficit to force overtime on Darius Morris' turnaround in the final minute of regulation.

"Neither team made shots," Self said. "That was a miserable display of shooting, but probably a pretty good display of both teams guarding."

It wasn't always pretty, but Kansas still came away with the victory, and after winning its first 15 games has its best start since beginning 20-0 in 2007-08. Morris and his twin brother Markieff both had double-doubles. Markieff Morris had 13 points and 11 rebounds, and Marcus had 10 rebounds to go along with his crucial scoring.

Their performance down low was important on a day neither team could shoot straight.

Michigan scored the last six points of regulation to tie the game at 51. Zack Novak then made a 3-pointer at the start of overtime to give the Wolverines their first lead of the game, but the Jayhawks scored the next eight points, all by the Morris brothers. Marcus Morris made two free throws, and Markieff put Kansas back in front to stay with a 3-pointer that made it 56-54.

A conventional three-point play by Marcus Morris gave the Jayhawks a five-point lead, and a 3-pointer by Tyrel Reed put Kansas up 62-56.

"We didn't think this was going to be an easy game -- and it wasn't," Kansas guard Tyshawn Taylor said. "We started off really good, but Michigan came back with a run."

The Wolverines trailed by 15 points in the first half and were down 41-28 in the second, but their 1-3-1 zone defense appeared to fluster Kansas at times even though the Jayhawks beat Michigan last season.

"We attacked it miserably," Self said. "We attacked it miserably last year too, and we meant to do some different things and we kind of reverted back and didn't attack. Of course, it doesn't help when you don't make shots, but that's about as bad as you can play against a zone, I think."

Kansas was playing its last nonconference game of the regular season before starting Big 12 play. Self improved to 8-0 against Michigan.

Darius Morris scored 16 points, and Novak added 12 points and 11 rebounds for Michigan. Freshman Tim Hardaway Jr. scored 19 points for the Wolverines but was only 5 of 19 from the field with his father, the former NBA star with the same name, looking on.

"He's playing much better than I thought he would," the elder Hardaway said. "He's surprising me by moving his feet on defense in one-on-one situations and he's just really progressing here."

The Jayhawks stifled Michigan's patient offense at the start, holding the Wolverines without a field goal for nearly 7 minutes. Kansas led 25-10 before Michigan went on an 8-0 run to finish the first half. Darius Morris made two three-point plays, and Novak barely beat the end of the shot clock with a baseline basket that ended a wild possession in which two Michigan players made key passes while on the ground.

The Wolverines shot 26 percent for the half.

Michigan's schedule won't get any easier after this near-upset. On Wednesday night, the Wolverines host No. 2 Ohio State, which is also undefeated.

"We can't let people pat us on the back about this," Hardaway Jr. said. "We have to keep a chip on our shoulder."

Travis Releford played only 4 minutes for Kansas. He was helped off in the first half with a left ankle injury.