Shannon Scott pulled the Buckeyes within 66-64 with a free throw with 28.9 seconds left before Quinn Cook sealed it by hitting six free throws in the final 27.3 seconds.
Cook finished with 12 points for Duke, which shot 58 percent in the second half to remain unbeaten at home in the ACC-Big Ten Challenge and preserve its school-record winning streak at home against nonconference opponents.
The Blue Devils who beat then-No. 3 Kentucky in Atlanta and then-No. 2 Louisville in the Bahamas won their 97th straight against non-ACC visitors to Cameron Indoor Stadium.
But for much of the way, nothing came easy for them. They were outrebounded 40-37, couldn't get anything going on the offensive glass, struggled to keep up with Ohio State's quick ball movement and couldn't find their touch.
Then came the flurry of 3-pointers that put them in control.
Sulaimon buried one from the key to pull the Blue Devils within 51-50 with about 6½ minutes left. Kelly then hit 3s on consecutive trips down the court, including one in Amir Williams' face that put Duke ahead to stay, 56-53 its first lead since the 14-minute mark of the first half.
Boise State 83, No. 11 Creighton 70 • At Omaha, Neb., after nearly winning on the road at Michigan State last week, the Broncos pulled the biggest upset in program history Wednesday night with their victory over Creighton.
Derrick Marks scored 28 of his career-high 35 points in the second half, bettering the 24 he had in the 74-70 loss to the 13th-ranked Spartans.
The Broncos (5-1) beat a ranked opponent for the first time in four seasons and on the road for the first time since March 2005.
• No. 2 Duke 73, No. 4 Ohio State 68
• No. 9 Arizona 93, Northern Arizona 50
• Boise State 83, No. 11 Creighton 70
• Miami 67, No. 13 Michigan State 59
• No. 22 Illinois 75, Georgia Tech 62
• No. 24 UNLV 85, UC Irvine 57
• No. 25 New Mexico 76, Mercer 58