Minnesota (4-1, 1-0 Big Ten) also got a 30-yard interception return for a touchdown by De'Vondre Campbell, highlighting a defensive effort that saw the Golden Gophers limit Michigan (2-3, 0-1 Big Ten) to 171 yards of total offense.
This is the first time Michigan has three losses in a season by the end of September in its 135-year football history, according to ESPN Stats & Information.
David Cobb accounted for 161 of Minnesota's 229 total yards in the first half, which ended with the first of three field goals by Ryan Santoso to give the Golden Gophers a 10-7 lead. Cobb finished with 183 yards rushing on 32 carries.
Michigan had just 106 yards of total offense and Morris had thrown eight consecutive incomplete passes when Gardner entered the game with 11:17 left in the fourth quarter.
Gardner led the Wolverines on 74-yard scoring drive in his first action, scoring himself on a 3-yard run to pull the Wolverines within 30-14 with 7:27 remaining in the game.
Michigan coach Brady Hoke stood by his decision to start Morris.
"Sometimes we want to point the finger at one guy because he's the quarterback and I don't think that's fair," Hoke said. "We have to do a better job with some protection things -- the pocket closed a couple times on him -- and the interception was a tipped ball at the line of scrimmage that got knocked up into the air."
Cobb turned a screen pass into a 33-yard gain to set up Minnesota's first score, a 10-yard rollout run by Leidner with 8:00 left in the second quarter that tied the game at 7-7.
The senior running back averaged 5.7 yards per carry against a Michigan defense that entered the game ranked ninth in the NCAA with rushing defense at 80.3 yards per game.
De'Veon Smith led Michigan with 57 yards rushing, including a 10-yard touchdown run.
In Minnesota's first visit to the Big House under coach Jerry Kill in 2011, the Gophers were rolled 58-0.
Last season, with Kill back in Minneapolis dealing with health issues, Michigan won 42-13.
"We watched film of that (2011 game) and it was like night and day the difference between what it's like now," said senior defensive tackle Cameron Botticelli, who had a sack and two tackles. "Words cannot describe how it feels to go from 58-0 then to winning (Saturday)."
Former Michigan coach Lloyd Carr's grandson Chad was named an honorary captain for Saturday's game. The 4-year-old has been diagnosed with an inoperable brain tumor.
The school says the Carr family is encouraging people to support pediatric brain cancer research -- (hash)ChadTough prayer brands were available Saturday at stores in Ann Arbor and online at mden.com. A $3 charge is going toward The Chad Tough Fund for pediatric brain cancer research at C.S. Mott Children's Hospital.
Chad Carr was recently diagnosed with diffuse intrinsic pontine glioma, a type of pediatric brain tumor.