The Golden Gophers (17-9, 7-6) ended a three-game losing streak, and were led by Vincent Grier with 14 points and 10 rebounds.
The Buckeyes (18-9, 7-6) were paced by Terence Dials' 17 points and eight boards.
Ohio State took a 50-49 lead on a short baseline jumper from J.J. Sullinger with 1:01 left in the second half.
Minnesota came right back to take the lead at 51-50 on a basket from J'son Stamper with 29.6 seconds remaining. Sullinger nearly had a steal on the entry pass to Stamper, but the ball took a fortuitous bounce (for UM) off the backboard, right to the awaiting Stamper.
Despite the bad luck, OSU still had a chance to win. But Dials missed a shot in the lane, which was rebounded by Minnesota's Aaron Robinson, who was fouled with 11.6 seconds left.
Robinson made one-of-two free throws for a 52-50 UM lead.
Following an OSU timeout at midcourt, Sullinger missed a short runner that would have tied the game with one second remaining. The ball caromed out of bounds as time expired.
The Buckeyes had a chance to retain sole possession of fourth place in the Big Ten, but they now have company as the Gophers swept the season series.
"The unfortunate thing for us is that we couldn't make shots throughout the game," OSU coach Thad Matta told WBNS radio. "Probably the first 32 minutes of the game, I thought we had some unbelievable looks and the ball just wouldn't go in. I give Minnesota's defense credit, but those are shots that we've got to knock down."
Minnesota led nearly throughout the first half – its largest advantage coming at 20-13 with 6:58 remaining in the half.
Ohio State was just one-of-eight from three-point range in the first half and the Gophers held a 24-19 lead at halftime. The score was eerily similar to the 24-18 halftime lead Minnesota held in its 60-56 overtime win over OSU in Columbus on Jan. 19.
Unlike the previous meeting, Minnesota came out on fire in the second half. It scored seven quick points to take its largest lead of the game at 31-19.
Ohio State then chipped away, cutting the deficit to six (37-31) at the 11:48 mark on a deep three-pointer from Jamar Butler. It was good from NBA range and then some.
But OSU could get no closer at that stage of the game. The teams traded buckets for the next several possessions and Minnesota led 47-40 with 6:32 left in the game.
Dials then brought OSU back within four, 47-43, with a three-point play at the 5:50 mark.
Ivan Harris followed that up with a three-pointer – his only points of the game – making the count 47-46 UM with 4:24 left.
Dials then gave the Buckeyes their first lead since the opening minutes of the game when he connected on a pair of free throws for a 48-47 advantage with 3:46 left.
Grier got the lead back for the Gophers when he drew a blocking foul on Dials and made two free throws for a 49-48 Minnesota lead with 1:23 remaining.
That was followed by Sullinger's basket off the drive to the baseline, but the Bucks were not able to hold the lead.
"I'm happy about our competitiveness and the comeback in this environment," Matta said. "You take the lead… and to lose a game where the ball hits you in the hands and goes off the backboard and they put it in. But I thought we had a great shot at the end to try and tie it up."
Dials, who continues to be plagued by foul problems, was the only Buckeye in double-figures in scoring. He finished with four fouls, but was productive when he was on the court. The team was playing without suspended forward Matt Sylvester, who usually provides scoring punch in his sixth-man role.
Tony Stockman had nine points off the bench. Sullinger added eight points and nine rebounds, and Butler also had eight points.
Jeff Hagen had 12 points and six boards for Minnesota.
Overall, OSU shot just 36 percent from the floor (19-of-53), including 31 percent from three-point range (5-of-16).
Minnesota shot 46 percent from the floor (20-of-44) and 27 percent from downtown (3-of-11).
Ohio State is now off for a week. It gets back in action Sunday, Feb. 29, when Wisconsin comes to Columbus for a 2 p.m. contest.
The Badgers (17-6, 8-4) did not play this weekend. Their most recent game was a 76-50 romp over Michigan Wednesday.