Ohio State wasted little time taking control of the game.
They ran off 11 points in a row after Jasmin Shuler opened the scoring with a three-pointer from the top of the key.
Ashley Adams scored the first basket of the season for the Buckeyes, a layup set up by a touch pass from freshman Kalpana Beach on a play started by Prahalis.
Prahalis gave Ohio State its first lead of the season with a pair of free throws, then Beach scored the first basket of her career by putting back a Prahalis miss.
Hill kept the run going with a three-pointer set up by an Adams offensive rebound, and Beach finished the spurt with a short jumper.
Destiney Gaston stopped the run with a Tennessee State layup, but that did not stop the bleeding for the Lady Tigers.
Adams answered with a layup to start another spurt, this one 12-0, with a layup that also featured five points by Raven Ferguson, layups from a Amber Stokes and Adams along with an Emilee Harmon free throw.
Once they took control, the Buckeyes never looked back. Their lead hit 20 points for the first time on a pull-up jumper by Prahalis at the 9:48 mark and reached 30 with a pair of free throws by freshman Shelbi Honeycutt with 4:20 left in the half.
The hosts played full-court man-to-man defense for much of the first half and forced 13 turnovers.
Ohio State head coach Jim Foster nearly emptied his bench in the first half. Twelve different Buckeyes saw the floor, everyone on the roster with the exception of redshirt freshman Amy Scullion. Scullion saw her practice time limited in the preseason by a sore Achilles tendon she hopes will not linger too long into the regular season.
The sharp opening half gave way to a choppy final 20 minutes, but Foster was satisfied with his young team's opening act.
"I thought we started the game very aggressively," he said. "It's difficult to play 12 people and continue to have continuity on offense. That probably showed in the second half. I thought we had some spurts where we really played well and shot the ball well from the foul line and rebounded well."
Ohio State's lead never dipped below 20 in the second half, but there was a tense moment when Prahalis went to the floor while trying to rebound her own missed layup around the nine-minute mark. A team trainer raced to her aid but initially seemed to make things worse when she grabbed Prahalis' right leg and stretched it. After calming Prahalis down a moment later, the trainer and another team staffer helped the point guard off the floor.
The worst fears of Ohio State fans were not realized, however, as she soon was up off the bench to join a huddle during the under-eight-minute media timeout.
"I got caught in the air and I think someone took me out and then I fell and someone stepped on my ear and then I cramped up," she explained afterward.
Prahalis returned to the game at the 5:36 mark and played the rest of the game.
That left only one more question for the 3,132 fans in attendance: Would the Buckeyes score 70 points and earn free french fries or apple slices from McDonald's for them?
The students section chanted their desire for the free fries several times before Beach satisfied them with a layup that made it 71-47 at the 3:55 mark.
Beach, a freshman from Westlake, Ohio, was a surprise starter and finished the day with 10 points and six rebounds. She was 4-4 from the free throw line and blocked a pair of shots.
"I knew it was going to be a lot different from high school so I was going to go out and play as hard as I could and try not to make too many mistakes," she said.
After shooting 53.1 percent in the opening half, the Buckeyes were only 9 for 22 (40.9 percent) in the second stanza, but they held the Lady Tigers to 31.7 percent shooting (20 for 63) overall.
Joining Beach in double figures were Adams and classmate Ferguson, both of whom had 10 points.
Adams also blocked six shots while Ferguson had eight rebounds and two assists in 21 minutes.