Ohio State forward Sarah Schulze made a three-pointer to kick off the run then added a layup. Teammate Jantel Lavender followed with a pair of buckets, and the Buckeyes led 14-7 with 14:05 to go in the first half.
Point guard Samantha Prahalis assisted on all four baskets then found her own scoring touch.
After Amanda Leigh made a three-pointer from the left wing for the Spartans (1-3), Prahalis made a layup to push the Ohio State advantage back to six.
UNC Greensboro's Kendra Smith answered with a trey to cut the lead go 16-13, then Prahalis drove through the Spartan defense for a layup to start an 8-0 Ohio State spurt.
She followed that with a fast-break layup then Lavender added two more baskets to push the Buckeyes' lead to double figures for the first time, 24-13, with 11:24 left in the half.
Leigh tried to keep the visitors in it with another trey, but the Buckeyes answered quickly again.
Prahalis set up Alison Jackson for a layup to give Ohio State a double-digit lead again, and the Buckeyes never looked back.
Beginning with Jackson's basket, they outscored UNC Greensboro 19-9 the rest of the half to take a 43-25 lead into the locker room.
The Buckeyes removed any doubt from the eventual outcome by outscoring their foes 20-4 in the opening eight minutes of the second half, a surge that put them ahead 63-29.
On the strength of a 19-point first half, Lavender led all scorers with 27 when all was said and done, and Prahalis added 13 points to go with 11 assists.
"Sammy had half of our assists and was moving the ball, and what's starting to happen is she's getting opportunities to get to the basket because teams have to respect our ability to shoot the three," Ohio State head coach Jim Foster said. "She's getting to the basket and the bigs will rotate over and then she finds Jantel and (Andrea Walker), so that's good stuff."
Schulze, who made all three of her shots from beyond the three-point arc, pitched in 11 points and seven rebounds, tying Lavender for the team lead in the latter category.
Jackson turned in a strong performance with six points and five rebounds in 15 minutes.
Twelve different players scored for the Buckeyes, who led by as many as 43.
"I want to make sure we have combinations of players out there that are going to play together as the season progresses," Foster said. "I really liked Alison Jackson with the first group out there today. I think Jantel and Sammy take care of their business. I want (Walker) to establish herself on the low block."
Ohio State scored 31 points off 21 Spartan turnovers, but that was surprisingly OK with Spartan coach Lynne Agee.
"We focused on taking care of the basketball. Playing at our mid-major level trying to be a press-and-run team, we have been trying to focus on cutting down our turnovers," said Agee, who noted the pregame goal was to commit no more than 20.
Reserve guard Amber Stokes had four of the Buckeyes' 10 steals.
Those who stayed for the entirety of the contest were treated with seeing the first basket of the career of Ohio State freshman Alexandra "Sasha" Dobranic, who hit a layup with 1:15 left in the game.
"Sash is a very popular player on our team and our players kept trying to find her for a shot and she kept throwing the ball to other people because she thought they had a better shot," Foster said. "You love that unselfishness, and then they figured out how to get her a field goal. It was a senior who figured it out. Cherise (Daniel) saw what she was doing and then gave her the opportunity."
Dobranic, a 6-4 native of Novi Sad, Serbia, also recorded her first assist and finished with two points and a rebound in four minutes.