The 20th-ranked Buckeyes opened their home slate with a 87-49 victory over the Bearcats, who fell to 1-1 after posting a 15-15 campaign a year ago.
Hill had 21 while Stokes and Ferguson added 16 apiece. Ferguson set her career high while Stokes tied hers.
They were in the middle of a ball movement bonanza that had Ohio State head coach Jim Foster smiling and Cincinnati head coach Jamelle Elliott shaking her head.
Center Ashley Adams helped facilitate by handing out seven assists, and hot shooting all around made the Bearcats think twice about paying extra attention to Hill, the Big Ten's leading scorer last season.
"It's hard because we have more than one person that can handle the ball," Hill said. "Our post players pass the ball so well it's hard to double team."
Ohio State took control down the stretch in the first half and never looked back.
The Buckeyes led 42-21 at the half Stokes leading the way with a dozen points. She had the first four then Ferguson added the next five with a fast-break layup and a three-pointer.
That made it 9-0 before the Bearcats got on the board. They were scoreless when the first media timeout came at the 15:19, but Jeanise Randolph broke the drought with a jumper four seconds later.
Dayeesha Hollins brought UC within four with a jumper in the lane at the 14:01 mark that made it 11-7, but the Buckeyes quickly stretched the lead to a dozen by outscoring the Bearcats 10-2 over the next couple of minutes.
Ohio State's lead breached 20 for the first time when Hill scored a layup courtesy a nice entry pass by Adams that made it 40-19 with 1:25 to go.
After Kayla Cook hit a pair of free throws for the Bearcats, Ferguson scored on a driving layup with 10 seconds left to set the first half score.
Ferguson and Hill both finished the first half with nine points.
The Buckeyes were stifling on defense and sharp on offense. They held Cincinnati to 26.7 percent (8 for 30) while hitting at a 77.3-percent clip (17 for 22) in the first 20 minutes.
The game was the home opener for the Buckeyes (1-1), who began the season by dropping a 57-51 decision to No. 7 Notre Dame on Friday in Charleston, S.C.
"You can tell they play really comfortable playing at home," Elliott said. "They shot the ball with confidence today. I've been coaching this game for a long time and I don't think I've ever been part of a game when one team shot 77 percent from the floor and missed five shots. It's hard to win games like that."
The Buckeyes cooled off in the second half but not much. They went 18 for 30 after intermission and ended the night 35 for 52 for a 67.3 field goal percentage.
The Bearcats (1-1) never really found their stroke, either, as they finished the night 19 for 64 (29.7 percent).
"I thought everybody was taking their time with their shots," Stokes said. "A lot of people were getting good looks and the defense was pretty good, too, so overall we did all right."
Hollins led Cincinnati with 15 points, but she struggled against the defense of Stokes. The Bearcat junior made 6 of 18 shots and pulled down five rebounds while forward Tiffany Turner added nine points and a game-high 11 rebounds.
Adams led Ohio State with 10 boards and seven points to go with the seven assists.
Ohio State improved to 16-3 in the all-time series with the Bearcats. The teams last played during the 2001 WNIT, a game the Buckeyes won 61-60.