Rachel Sheffer made two free throws with 29.2 seconds left to complete Michigan's comeback from a 13-point halftime deficit.
Alison Jackson had a chance to put the Buckeyes back on top but missed two free throws with 3.4 seconds left.
After Michigan guard Jenny Ryan hit two more from the charity stripe, Ohio State's Brittany Johnson missed a desperation three from well beyond the three-point line, giving Michigan its second win against the Buckeyes this season.
The Wolverines (13-7, 6-2) swept the season series against Ohio State (13-7, 4-4) for the first time in school history. They won in Columbus for the first time since Jan. 21, 2001.
The 24th-ranked Buckeyes had a three-game winning streak snapped and saw a chance to continue their climb back to the top of the Big Ten standings dashed.
They were two games behind conference-leading Michigan State when the night began.
"It seems to me everybody is beating everybody, but it doesn't do you any good to lose to the same team twice," said Ohio State head coach Jim Foster.
It is hard to imagine the 3,440 fans at Value City Arena envisioned such a decision when the Buckeyes took a 46-33 lead into the locker room at halftime.
Both teams came out shooting hot, especially from beyond the three-point line, and the game was tied at 25 after Michigan's Kate Thompson made a three-pointer with 8:57 to go.
That was when Ohio State opened up some breathing room.
Ohio State's advantage reached double digits for the first time when Brittany Johnson scored off an inbound play with 1:20 to go, and Prahalis put an exclamation point on an outstanding half by nailing a three just before time expired.
It swished through the nylon to keep her perfect half intact and give Ohio State a commanding 46-33 lead.
Prahalis was 7 for 7 from the field, including five threes, in the opening 20 minutes and scored 19 points.
The Wolverines opened by making 8 of 12 from long range, but Ohio State trumped that with a 9 for 14 performance.
The second half was a different story.
The Buckeyes made only 2 of 7 threes and were 7 for 26 overall, a dismal 26.9 percent from the field.
They compounded their problems with 11 turnovers, and Michigan took advantage with 13 points.
One of those giveaways came at the 16-minute mark when Prahalis was whistled for charging under the basket. Her third personal foul, it sent the junior point guard to the bench with her team leading 49-37.
By the time she came back, the Wolverines had cut the lead in half, to 53-47 with 10 minutes to go.
They were still down six with three minutes left, but Ryan cut the deficit to four with a pair of free throws and Veronica Hicks made it two with a jumper at the 2:12 mark.
Prahalis nailed a jumper 29 seconds later, but that was the last time the Buckeyes would score.
Sheffer took the ball at All-America center Lavender, made a layup and drew a foul on the OSU star with 1:23 left. She made the ensuing free throw to bring her team within one, then Ohio State failed on two chances to extend the lead as Prahalis and Johnson both missed jumpers.
At the other end, Michigan again went to Sheffer, who drew a crowd under the basket and a shooting foul on Alison Jackson to set up the winning free throws.
Foster denied the suggestion the game was a tale of two halves.
"I wasn't real happy with our first half other than we made shots," Foster said. "We're not a team that can live and die by the three, and we never established Jantel through the course of the game.
"When it got tighter and we needed her to be there we were taking too many outside shots."
Michigan swarmed Lavender all night with two and three defenders, a strategy that held her to 10 points on 4-for-10 shooting. She was also charged with five turnovers.
Prahalis had 25 points and six assists but gave the ball away five times. She admitted the Wolverine defense left the Buckeyes frustrated.
"People sit in the lane but it's hard to find her," Prahalis said.
Added Lavender, "Like coach said, when I did have some open looks the ball didn't get there good or sometimes it didn't come at all. I don't think we reversed the ball well enough. It's frustrating when you're not doing what you're used to doing."
Sheffer, a 6-1 sophomore center, finished with 23 points, including 15 in the second half when Michigan went cold from the perimeter.
The Wolverines made only 2 of 10 treys after halftime, but Foster credited their consistent offensive approach with allowing them to put up 36 points.
"They hit 10 threes but they never forgot the post," the Ohio State coach said.
The lone bright spot from an Ohio State perspective was Lavender's 14 rebounds, a total that gives her 1,279 for her career. That is six more than the previous Big Ten record that was held by Denise Jackson of Indiana.
"It's exciting," she said, although her tone seemed to understandably indicate otherwise. "I'm glad I did it. I think it's awesome that it hasn't been broken in 26 years. I just rebound hard, try to get every rebound."