Dexter Dancs got the Wolverines on the board early, but Mittelstadt answered, beating Michigan goalie Hayden Lavigne with a long shot from the top of the left circle to make it 1-1 at 2:21 of the first period.
But Michigan kept coming, scoring two more goals in the first period and chasing sophomore goalie Mat Robson from the crease.
Junior Eric Schierhorn didn’t fare much better, surrendering a goal late in the second period after Gophers forward Scott Reedy cut Michigan’s lead to 3-2.
Brannon McManus made it 4-3 with less than four minutes to play, before a tripping call on Michigan’s Dakota Raabe gave Minnesota a power play and a chance to tie the game with less than a minute remaining.
However, Michigan’s Brendan Warren derailed the Gophers’ comeback attempt just 13 seconds into the power play, scoring an empty-net goal to make it 5-3.
The Gophers, now 13-11-1 overall and 4-8-1-1 in conference play, have struggled against Big Ten competition this season. Minnesota has lost four Big Ten matchups in a row, and last claimed a conference win on Dec. 1, when they beat Wisconsin in Minneapolis.
Minnesota and Michigan square off again Saturday at 7 p.m.