"I hit one of the biggest shots I've hit in college," said Connolly, who missed his first three attempts from 3-point range.
Williams was boxed in on the Illini's last shot and his long attempt from in front of the Illinois bench fell short. Hundreds of fans flooded the floor at Value City Arena after the final buzzer.
With Illinois on top 61-60, the Buckeyes' Brent Darby was guarded by Sergio McClain in the backcourt and couldn't find an open man. But he was able to toss a pass to the left wing where Connolly broke open along the baseline. He turned and hit the 3-pointer to put Ohio State ahead 63-61.
"I came off a couple of screens and just came open," said Connolly, a transfer from Providence in his first year with the Buckeyes. "It felt like it was going in when it left my hand."
Williams, who had beaten Ohio State in the Big Ten opener a year ago with a 3-pointer at the buzzer, took the inbounds pass and dribbled to the left wing. Pressured by three defenders, his shot with two seconds left never was close.
"They did a good job of trapping me and they did a goo job of making it so I couldn't see anyone to pass to," Williams said.
The Illini (21-6, 11-3) came in on a five-game winning streak and still lead Michigan State (10-3) by a half-game in the conference.
"We thought they would double Frank and take him away and we would use Cory Bradford to back him," Illinois coach Bill Self said. "They just did a great job on defense. We couldn't get the ball where we wanted it."
Ohio State (18-9, 9-5) had lost its first four games against ranked teams this season, but has now knocked off four ranked teams in the last month including another team that was No. 3 at the time, Michigan State.
"How about our kids?" Buckeyes coach Jim O'Brien said. "They hung in there, they didn't lose their composure and they just toughed it out. We had to play like we did against Michigan State - anything else and we lose."
Brian Brown led Ohio State with 18 points, while Ken Johnson had 16 points and Darby had 14. The Buckeyes have won five straight Big conference games.
"They're good, but we were up by one with 35 seconds left and didn't get it done," Self said. "It was nobody's fault. Connolly just made a great shot."
Johnson, honored earlier as the Buckeyes' only senior, blocked two shots to tie former Penn State center Calvin Booth for the most career blocks by a Big Ten player (428).
Williams scored 22 points and Marcus Griffin had 12 for the Illini, who had won 14 of the last 16 meetings with Ohio State.
Johnson's slam dunk to open the second half gave Ohio State a 38-29 lead. But Illinois came back with the next 12 points, holding the Buckeyes without a point for more than six minutes. Williams scored the first three baskets and assisted on two others in the surge, while Ohio State missed eight consecutive shots.
Johnson became the 39th Ohio State player to score 1,000 points in a career when he hit a free throw with 7:31 left that gave the Buckeyes a 52-45 lead.
Illinois drew even at 56 on Sean Harrington's 3-pointer from the right wing with 4:01 remaining.
Boban Savovic responded with a 3-pointer and a free throw to put the Buckeyes up 60-56 with 3:44 to play.
Williams then converted a three-point play, and after an Ohio State miss, hit a 10-foot fadeaway for a 61-60 lead to set up the wild finish.
"This is the best feeling I've ever had here," Johnson said. "It was everybody's heart. It was a terrific game on everybody's part."
Asked about the fans who ran onto the floor after the final buzzer, O'Brien grinned.
"Anyone who beats them deserves to rush the floor," he said. "That's the price Illinois pays for having a great program."
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