Alli Smalley's three-pointer after a jump stop with 25 seconds left tied the game at 75-75 with 25 seconds left to play in regulation.
The 20th-ranked Tigers then got a defensive stop to send the game into overtime.
"We actually worked on it (the play for the game-tying shot) right before the game," said Smalley, who added she probably played the best game of her college career. "Sherell (Hobbs) and Jordan (Greenleaf) set really good screens on the girl and I came off of it.
Smalley wasn't thinking about the late three-pointer being the key to winning the game. "I just caught it and shot it," she said.
Senior Whitney Boddie, who scored 14 points and dished out 11 assists, got the first basket of overtime and the Tigers pulled away from there. "It was a signature win for us," said the point guard, who said the Tigers have a team goal to not lose a home game this season.
Smalley scored on a fastbreak basket to stretch the lead to four early in the overtime, but the Buckeyes cut the lead to 79-78 on a three-point shot by Ashlee Treblicock, who got an uncontested shot from the corner when a loose ball bounced her way.
Back-to-back baskets by Sherell Hobbs, who matched Smalley for game-high scoring honors with 23 points, stretched the Auburn lead to 83-78 with three minutes left to play in the overtime.
A double-clutch fastbreak layup by Smalley increased the lead to seven points and the Tigers came away with a sweep of the home-and-home series with the Buckeyes.
Asked about the key to the overtime, Hobbs said, "The defensive intensity was great. We ran the floor good. All of those drills we ran this summer paid off in the end."
Auburn improved to 4-0 this season while Ohio State fell to 3-1.
The shooting percentages were nearly identical. Auburn hit 41.8 percent from the field while Ohio State finished at 41.9 percent.
Auburn was 13-18 at the foul line and 8-17 on threes. Ohio State was 10-15 at the foul line and 8-20 on threes. Smalley hit five of the threes for the Tigers on 10 attempts behind the arc.
Jantel Lavender, a 6-4 sophomore, led the Buckeyes with 20 points and 12 rebounds, but she took 27 shots to score that many points. Star freshman point guard Samantha Prahalis added 15 points and eight assists.
Auburn got 17 points and 11 rebounds from its star, DeWanna Bonner, who played with an upper respiratory problem but was on the court for 40 of the game's 45 minutes.
Auburn forced 23 turnovers and had eight fewer than the Buckeyes, which allowed the Tigers to overcome being out-rebounded 49-46.
Auburn coach Nell Fortner said, "I thought what happened today is we saw our veterans really do what veterans do. That has been a long time coming for us. These kids have worked hard.
"DeWanna and Whitney have been starters for us since they were freshmen," the coach added. "Sherell Hobbs and, oh man...our veterans stepped up. Alli Smalley played like a veteran today. I think that is why we won the ball game. We played some good basketball down the stretch."
The first half was close all of the way. Both teams came out making everything they shot, but cooled from the field and had almost identical shooting performances. The Buckeyes made 16-37 first half field goals while Auburn made 16-36.
The Tigers led 42-38 at halftime thanks to having just five turnovers, six less than the visitors. Bonner led the Tigers in scoring at halftime with 11 points while Hobbs had nine and Boddie had eight.
Auburn stretched the lead 53-42 on a layup by Bonner with 15:28 left in the game, but the Tigers went cold on offense after that.
Ohio State took advantage and pulled ahead on a layup by Lavender with 9:21 to play to make the score 57-56. The lead grew to 63-56 with 7:29 to play on another layup by Lavender.
However, Auburn outscored the Buckeyes 9-4 in the last 2:31 to tie the contest.