Playing her final game at Value City Arena, senior Tayler Hill led all scorers with 20 points while Raven Ferguson (13), Ameryst Alston (12) and Ashley Adams (12) also scored in double figures for the Buckeyes.
After Ohio State opened up an early 11-6 lead, the Wolverines battled back to tie the game at 16 with a layup by Sam Arnold at the 9:40 mark.
The Buckeyes then scored 10 of the next 12 to open up an eight-point lead, their largest of the half.
Adams started the sequence with a short jumper set up by a feed from Hill, who followed with a pair of free throws. After a Rachel Sheffer basket for Michigan, the Buckeyes tacked on the next six with an old-fashioned three-point play by reserve forward Darryce Moore and a swish from beyond the three-point line by Ferguson, who was wide open in the corner in front of the Michigan basket thanks to a drive dish by Amber Stokes.
Michigan cut the deficit to three with two minutes to go before Adams closed out the half by putting back a Hill miss with three seconds left.
The Buckeyes took a 30-25 advantage into the locker room thanks to a balanced scoring effort that saw six players connect from the field.
Freshman point guard Alston led the way with nine points while Hill added seven and Adams notched six.
Sheffer and guard Kate Thompson had six apiece for the Wolverines.
The Buckeyes never trailed in the second half, but they had to hold off a Michigan (20-9, 9-7) squad hoping to remove itself from the NCAA tournament bubble.
Michigan cut the lead to one three times in the last 15 minutes, first on a layup by Sheffer at the 14:31 mark, then on three-pointer by Arnold 45 seconds later and a Nya Jordan layup with 11:39 to go.
An Ohio State team that has struggled to score for much of the season had an answer every time, however.
First came a three-pointer by Alston from the wing then a slash through the lane for a layup by Hill, who also met the last challenge with a three-pointer of her own.
The game remained tight heading into the final two minutes when the Buckeyes finally pulled away.
Ferguson hit a pair of free throws with 2:04 left to stretch a five-point lead to seven, 58-51.
After a Michigan layup by Jordan, Hill cut through the heart of the Wolverine defense for an acrobatic layup that made it a seven-point game.
Stokes pressured Ryan into a bad pass that was picked off by Alston, who started a break that Ferguson finished with a layup that sent the season-high crowd of 7,793 fans at Value City Arena into a frenzy gave the Buckeyes a nine-point lead, their largest to that point.
After Ferguson's basket, Foster called timeout to put into the game Emilee Harmon, a senior who had not played to that point.
The Buckeyes closed the game out with a pair of free throws and an Adams layup sandwiched around a Thompson jumper, but that was academic.
The 11-point win over a 20-win club gave Ohio State a three-game winning streak to end what was often a trying regular season.
It also revived some talk the Buckeyes (17-12, 7-9) could earn an at-large bid to the NCAA tournament, but they likely remain a long shot at best as they entered the day 69th in RPI according to realtimeRPI.com
A sub-.500 record in conference play and lack of a marquee nonconference win could ultimately be Ohio State's undoing, but the tournament committee could take into account their 1-3 mark in January without Stokes, who missed four games with a sprained left knee.
Before that decision is made, Ohio State opens postseason play Thursday in the Big Ten tournament in suburban Chicago.
With his team on a three-game winning streak, Foster confirmed the Buckeyes are playing their best basketball at the conclusion of the regular season.
"It's good to have Amber healthy or healthier putting pressure on the ball," he said. "We've got multiple people scoring now and that makes us hard to play."
Sheffer led Michigan with 19 points while Thompson and Jordan had 10 apiece.
The Buckeyes notched 18 assists while committing only six turnovers. They also shot 54.3 percent from the field (25 for 46) in what was in nearly all manner their most efficient offensive performance of the season.
After the game, Hill, Stokes, Harmon and Briana Sanders were recognized in a Senior Day ceremony.
Sanders has spent the past two seasons as a student coach after knee problems ended her playing career.