"I had a feeling I was going to get the ball," said Conley, son of the 1992 Olympic triple-jump gold medalist. "I just went to the hole and it worked out for us."
With the victory, the Buckeyes are likely to climb to the top spot in The Associated Press rankings for the first time since Jerry Lucas, John Havlicek and a sub named Bob Knight were ranked No. 1 throughout the 1962 season.
"I hope it motivates us," coach Thad Matta said. "I hope it continues to pour gas on our fire."
Alando Tucker, Wisconsin's candidate for conference player of the year, had given the Badgers the lead with just under a minute left when he scored inside off Jason Chappell's dump pass.
Chappell then blocked a shot by Ron Lewis before Wisconsin's Kammron Taylor was sent to the line in the bonus situation with 20.3 seconds left. Taylor's first attempt spun off the rim.
After a timeout, the Buckeyes (26-3, 14-1) passed around the perimeter before Conley, a freshman who has spent his career in the shadow of 7-foot high school and college teammate Oden, scissored through the lane and tossed up a soft shot that balanced on the rim before falling.
"If you've got a point guard like Conley, he's going to try to penetrate," Wisconsin coach Bo Ryan said. "We were trying to make him take a tough shot."
The Badgers (26-4, 12-3), who lost both games this week after becoming No. 1 for the first time ever, inbounded to Taylor who drove the length of the floor and tried an off-balance 15-footer at the buzzer. Oden got a piece of it before Lewis, a senior playing his final home game, swatted it away.
"I didn't know I was going to block it until he put it right in my face," Lewis said with a wide grin while wearing a Big Ten championship hat and T-shirt.
Taylor looked to the officials, hoping to hear a whistle. But there was no call and within seconds a capacity crowd flooded the court in celebration.
"I was just trying to get to the basket and draw some contact but it didn't work out," a disconsolate Taylor said. "It feels bad. We worked so hard, and then to have it go through your hands like that _ it hurts."
Ivan Harris led the Buckeyes with 13 points, with Oden and Conley each scoring 11.
Amid speculation he might turn pro after his freshman year, the crowd serenaded Oden with a chant of "One More Year!" as the Buckeyes assembled on the floor to accept the conference championship trophy.
"I thought they were talking about Ivan!" Oden cracked.
Pressed for an answer, he said, "That's a decision that's going to be made later on in the year."
Tucker, averaging 20.2 points, was held to 12. Reserve Jason Bohannon went 3-for-3 from 3-point range and finished with 11 points. Taylor scored 10.
Ohio State also won the last time a No. 1 team visited Columbus _ stunning unbeaten Illinois in the home finale two years ago.
The Buckeyes have won 12 straight conference games and 25 in a row at home, including all 18 this season.
In a tense, gritty yet typical Big Ten defensive struggle, Wisconsin grabbed a 46-42 lead before Conley converted a 12-foot right-handed jumper _ he usually shoots left-handed. After an errant alley-oop pass by Chappell, Conley drove the lane and dished to Oden, who retrieved the loose ball and dunked while he was being fouled. He then completed the three-point play for a 47-46 lead with 2:46 left.
With just under a minute left, the Badgers pulled Oden away from the basket as he guarded Chappell, who dumped a pass inside to Tucker for a layup to set up the final, hectic minte.
"It came down to the last play and the guy made a tough shot. You can't hang your head on that," Tucker said. "The thing that gets me is we were in position to put the icing on it and a defensive stop that we pride ourselves in, we didn't get it."
The Badgers lost their tallest starter and leading rebounder, Brian Butch, for the entire second half after he sustained an elbow injury midway through the opening half.
Ohio State captured back-to-back outright titles for the first time since running off three in a row between 1960-62.
Wisconsin was No. 1 in the poll for the first time ever, but then lost at Michigan State 64-55 on Tuesday night. The Badgers won the first matchup between the teams 72-69 on Jan. 9 in Madison.
"We've got another game, at home," Ryan said of the season-ending rematch against the Spartans on Saturday. "We'll take a day off to rest, then get back at it. We'll get after it."