The fourth-ranked Buckeyes (20-1, 8-0) led by five, 32-27, after a tightly contested first half played before 2,518 at Crisler Arena.
Tayler Hill assisted on both baskets, and with their largest lead of the night, the Buckeyes looked poised to take control.
The Wolverines (10-8, 2-6) were far from finished, however. They scored nine straight points - the first seven by Carmen Reynolds - to draw within one.
Jantel Lavender countered with a basket for Ohio State, but then Michigan rattled off 10 more in a row. This time, freshman Dayeesha Hollins did the bulk of the damage with a three-pointer and a pair of twos that prompted Ohio State head coach Jim Foster to call timeout with his team trailing 43-39 and 12:12 remaining in the game.
The Buckeyes failed to score on their first possession out of the timeout, though, and Michigan stretched its lead to seven with a trey by 6-6 center Krista Phillips.
Lavender made one free throw to end Ohio State's scoring drought, and while the Buckeyes continued to languish on the offensive end, they finally started to get stops at the other.
Ohio State went nearly six minutes without a field goal until Andrea Walker made a layup with 8:42 left that cut the Michigan lead to four, and though Veronica Hicks answered that with a pair of free throws to make it 48-42 Wolverines, the Buckeyes finally got something going on the offensive end.
The cut their deficit to 50-49 then went ahead 51-50 thanks to another Walker layup with 6:07 to go.
Reynolds answered that with a three-pointer, then Lavender put the Buckeyes back on top with a three-point play inside. Prahalis followed with a basket and Lavender scored again to stretch Ohio State's advantage to five.
Reynolds made another trey to draw the Wolverines back within two, 58-56, but neither team scored in the final 2:49.
Michigan had a chance to tie the game or take the lead with an inbound under its own basket in the final seconds, but Ann Arbor native Shavelle Little stole the ball from Reynolds with six seconds left.
Lavender led Ohio State with 20 points, and the junior center added 10 rebounds for her 48th career double-double.
Prahalis added 13 points and nine assists. Johnson had eight.
Reynolds, a sophomore forward from Hilliard Davidson High School in suburban Columbus, led Michigan with 20 points. She made 7 of 21 shots, including 4 of 12 three-pointers.
Hollins had 11 points but finished with as many field goals (five) as turnovers.
Ohio State beat Michigan for the 14th consecutive time and improved to 22-4 at Crisler Arena, where the Buckeyes last lost Jan. 29, 1999.
The Buckeyes downed the Wolverines 59-56 on Jan. 3 in Columbus.