Batteast scored seven points as the Irish ended the game with a 12-0 run after trailing 62-54 with 4:39 left. The senior All-America forward blocked a potential tying 3-pointer by Ohio State's Caity Matter with 2 seconds left.
The Irish, who beat No. 6 Duke in the WNIT semifinal Wednesday, beat top 10 teams in back-to-back games for the first time since beating No. 1 Connecticut and No. 9 Purdue in the Final Four to win the national championship in 2001.
Batteast, who was 10 of 12 from the free-throw line, made a pair of free throws to start the comeback for the Irish (4-0).
She converted a three-point play with 3:59 left to cut the lead to 62-59. Megan Duffy, who had 15 points, hit a 3-pointer to tie it and Batteast put the Irish ahead for good on a 12-foot jumper that bounced twice off the rim before falling in.
The Buckeyes (3-1), who set a Preseason WNIT single-game record with 13 3-pointers against Bowling Green, and set a tournament mark with 27 3s in the four-game tournament, missed their final two 3-point attempts.
Batteast also scored 10 straight points midway through the first half to give the Irish a 21-12 lead.
But Ohio State, which trailed 29-25 at halftime, appeared to have the game under control as Jessica Davenport scored 14 of her 23 points in the second half and dominated in the middle. She also was 9 of 9 from the free-throw line, but was held without a point after scoring inside over Teresa Borton with 6:42 left.
Ashley Allen hit a 3-pointer to give the Buckeyes a 60-54 lead, and Matter, who had 13 points, drove in for a layup to make it 62-54.
But Ohio State missed its final eight shots down the stretch and turned the ball over four times.
Batteast was named the MVP of the tournament. Teammate Megan Duffy was named to the WNIT all-tournament team, as was Ohio State's Davenport and Matter; Monique Currie of Duke; and Shawntinice Polk of Arizona.