Amadeo Della Valle added 11 points for the Buckeyes (17-5, 4-5 Big Ten) in a bruising back-and-forth affair with the Badgers (17-5, 4-5).
Sam Dekker missed a 3 at the buzzer for Wisconsin, which suffered a third straight home loss.
The Badgers had plenty of chances to win but went just 5 of 10 from the foul line late.
Craft didn't hit his first bucket until 3:53 left, but it was 3 that helped his team finish on an 11-4 run.
Freshman Nigel Hayes led the Badgers with 17 points.
Wisconsin is free-falling down the Big Ten standings with its fifth loss in six games after a school-record 16-0 start.
Ohio State was in a similar spot coming into the afternoon after losing five of six following a 15-0 start.
Coach Thad Matta was looking for more mental and physical toughness from his team after an overtime loss at home earlier in the week to Penn State, and his Buckeyes shined at the hostile Kohl Center.
The Buckeyes didn't take the lead for good until Amir Williams (nine points, six rebounds) went 1 of 2 from the line with 54 seconds left for a 58-57 lead.
Both teams struggled with foul shooting, though it hurt Wisconsin more in the end.
Still, the Badgers had one last chance with 8 seconds left, but Dekker missed his rushed 3 from the wing.
The Buckeyes breathed a collective sigh of relief after whiffing on an easy chance to extend the lead on the previous possession.
Lenzelle Smith Jr., got the ball in transition after Traevon Jackson missed a free throw but missed a layup, then slipped after getting the offensive rebound to turn the ball over.
Luckily for Matta, the savvy Craft came up big late. Craft scored seven straight for the Buckeyes starting with his 3.
His play helped quiet a crowd that was electrified by Hayes in the second half, who has turned into Wisconsin's best scoring option in the frontcourt the last few games.
But Wisconsin couldn't capitalize. Ryan's team has lost three straight at home for the first time since 1997-98.
The offense is struggling for key stretches after playing so well earlier this season. Dekker finished with four points on 2 of 6 shooting. Ben Brust finished with 13 points and seven boards.
Things looked good early for the Badgers, even with leading scorer Dekker in foul trouble in the first half.
The last play epitomized Wisconsin's successful formula. Traevon Jackson missed a layup, but Frank Kaminsky swooped in for a one-handed offensive rebound and in the same motion tipped the ball to Brust. The guard converted for quick bucket and a 33-29 at the break.