The visiting Bulldogs scored the first nine points of the game and led 14-2 after 4:45, at which point Ohio State head coach Jim Foster replaced starters Brittany Johnson and Sarah Schulze with Shavelle Little and Andrea Walker.
Over the next four minutes, the seventh-ranked Buckeyes went on a slow-developing 11-0 run to draw within one, 14-13, with 11:20 left in the first half.
Gabrielle Williams scored for Alabama A&M (4-4) to stretch the lead back to three, then Samantha Prahalis set up Hill for a layup she finished in traffic.
The Buckeyes (12-1) took their first lead of the night at the 10:36 mark after Prahalis stepped in a passing lane for a steal then raced to the other end for a layup.
From that point, the Buckeyes never trailed but could not build much breathing room the rest of the opening stanza. Their largest lead was seven after a Prahalis jumper with 1:17 to go until halftime, but Katrich Williams set the halftime score with a jumper with 37 seconds left.
The Buckeyes led 34-29 at the break with Lavender pacing Ohio State scorers with nine points. Prahalis nipped at her heels with eight markers to go along with six assists and a steal.
Dominisha Johnson had 10 in the first half for the Bulldogs, who shot just 37.5 percent from the floor and committed 14 turnovers the Buckeyes converted to 15 points.
"We have a tendency to sort of have a negative connotation about what we didn't do," Foster said. "I think they did some good things today. They got off to a good start. I think we started the game shooting jump shots, and that's not a good way for us to start a game. They were open looks, but we've got a pretty good presence down low. We're really good when we play inside-out."
Although the Bulldogs never led after intermission, the Buckeyes needed more than half of the second half to put them away.
Prahalis gave Ohio State its first 10-point lead, 48-38, with a three-pointer at the 12:10 mark but the Bulldogs were able to hang around in the 12-point-deficit range until six minutes remained, when Ohio State went on a 12-0 run to remove any doubt about the outcome in front of 2,603 fans.
Walker scored a layup on a pass from Little to start the sequence, and Walker set up Cherise Daniel for another layup to cap it. In between, Hill had a pair of baskets and Lavender added a layup. Prahalis had two points, two assists and two steals.
Lavender led all scorers with 23 points. The Buckeyes' center added 11 rebounds for the 44th double-double of her career.
Prahalis had 16 points and 12 assists while playing her usual role of catalyst for the Ohio State offense. The point guard had three thefts and hit a pair of three-pointers.
"Once you let Samantha get started it's hard to stop her," Alabama A&M coach Altherias Warmley said. "It's kind of her show then. She did a good job of taking charge. You could see a great team coming together at that 10-minute mark, and at that point nothing we did was right."
Hill, a freshman starter at guard, found her way into double figures in the scoring with 11 points, but her contributions were greater than her stats indicated as she made several hustle plays and was disruptive on the defensive end.
"Tayler had a good burst in the first half and did some very good things for us," Foster said.
Little was her usual pesky self on the defensive end and finished with three steals and six points in 18 minutes.
Walker had 12 points and seven rebounds, and Foster sounded grateful to have options such as Little and Walker on his bench.
"We didn't get a very good start. We didn't make threes and we scored 78 points. I think we've come a long way that we can have Sarah and Brittany be a little out of kilter and Shavelle, Andrea Walker and Alison Jackson come in and score points for us," Foster said. "Obviously Shavelle is the two-time Big Ten defensive player of the year for a reason, and Andrea Walker with her length and she does the right thing more often than not in the framework of defense."
Although slow starts have been something of a problem all season for the Buckeyes, Prahalis said she never panicked.
"I just think we got off to a slow start, not a lot of energy," she said after recording her fifth double-double. "I kind of knew once we picked it up, we'd be all right."