Kevin Obanor 30 points and Max Abmas added 29 as the Golden Eagles became the ninth No. 15 seed to win an NCAA Tournament game and the first since 2016.
ORU led for more than half the game, but Ohio State moved out to a four-point lead with 2:34 to go.
Obanor erased that by hitting a pair of free throws twice, the second time with 14 seconds left.
Ohio State had a chance to win it in regulation, but Duane Washington Jr.’s step-back jumper was off-target at the buzzer.
“We were just trying to get in space and get downhill, yeah,” Ohio State coach Chris Holtmann said of that play. “We were trying to get him in space, get him to his left hand, get downhill off of a ghost action.”
Washington also had a chance to tie the game at the end of overtime but missed another trey as time wound down.
E.J. Liddell led Ohio State with 23 points while Washington had 18 and CJ Walker had 12.
Ohio State last lost in the first round of the NCAA Tournament in 2014 when Dayton knocked the Buckeyes out en route to an Elite Eight appearance.
They won their first tournament game in each of the first two appearances under Holtmann.
“I thought our guys had a terrific season,” Holtmann said afterward. “This is obviously a really, really bitter, bitter end to a terrific season, but we’ll own that and accept it, and we’ll move forward.”
This time around, Oral Roberts pulled off the upset despite shooting just 36 percent from the floor.
The Golden Eagles helped themselves by making 11 of 35 three-pointers and went 14 for 18 from the free throw line.
Ohio State missed half its 18 free throws and was just 5 for 23 from 3-point range. The Buckeyes shot 43 percent (29 for 67) overall.
The marquee matchup of Abmas, the nation’s leading scorer, against Washington never quite materialized.
Neither shot the ball well as Abmas was 10 for 24 from the floor and Washington went just 7 for 21. Abmas was 5 for 10 from 3-point range while Washington went 3 for 12.
Big men stole the show as Obanor took advantage of the undersized Buckeyes and made numerous big plays late in regulation and overtime.
He had 11 rebounds and went 7 for 7 from the charity stripe.
Liddell, Ohio State’s All-Big Ten sophomore forward, was 10 for 15 from the field and had 14 rebounds, but he also committed five turnovers while dealing with what appeared to be a back issue aggravated early in the second half.
“It was a tough matchup for him defensively because of how we had the switch,” Holtmann said. “It was a tough matchup for us, tough matchup for him. He had to expend a lot of energy at the other end. They’re really good, and their two players are really good in those pick-and-roll spots.
“I’m proud of E.J., proud of the sophomore year he had, proud of the kid he is. He had a tremendous sophomore year.”
The last No. 15 to win was Middle Tennessee State, which upset Michigan State in 2016.