The 19th-ranked Buckeyes (18-6, 9-4) snapped a three-game road losing streak and stayed within a game of first-place Iowa in the Big Ten standings.
They did so thanks to turning up the defense and taking better care of the ball after an intermission in which they trailed 42-31.
The Badgers (11-11, 4-8) shot 36 percent – 10 for 28 – from the field after halftime and were 0 for 6 from three-point range after making 4 of 8 deep shots in the first half.
After committing 11 turnovers in the first 20 minutes, Ohio State was guilty of just four in the second half.
Seniors Marscilla Packer and Tamarah Riley stepped up for the Buckeyes in the second half with 25 points combined, including 16 for Packer. Both were playing their first game since being benched for most of the second half of a 68-67 loss at Purdue in the Buckeyes' previous game on Feb. 7.
For the game, Packer was the high scorer with 23 points. She made 4 of 7 three-pointers and was 8 of 18 from the floor overall.
Following close behind her was Jantel Lavender, who poured in 22 points and grabbed seven rebounds.
Riley finished with 11, while Ashlee Trebilcock had nine.
In the final seconds, it was Anderson's three-point try that would have tied it had it been good, but the Buckeyes survived.
The Badgers took a 42-31 lead into the locker room at halftime thanks in large part to Banks, who torched the Buckeyes for 18 points.
Anderson had eight points and six assists in the opening stanza.
Lavender led Ohio State at the half with nine points while Packer added seven and Shavelle Little had five.
Wisconsin outscored Ohio State 12-3 from the perimeter and 10-2 at the free throw line in the first half.