The Cavaliers (4-4) faced a ranked team for the fourth game in a row and fell to 1-3 in those contests.
Ohio State (6-0) built a 21-7 lead in the opening 7:16 before Virginia mounted a 9-0 spurt to draw within five points with 8:45 to go in the half.
After the teams traded empty possessions, Ohio State guard Tayler Hill came up with a steal then threw ahead to Prahalis, who was all alone at the other end and made an easy fast-break layup to extend the lead to nine again.
Back to back threes by Lexie Gerson quickly pulled Virginia within three, and the Buckeyes looked like they were in for a dogfight, but they kicked hard to finish the half.
Ohio State shut out the Cavaliers over the last 3:13 of the first half and stretched a four-point lead into a 40-26 halftime advantage thanks mostly to a combination of offensive rebounding and tough defense.
With the Buckeyes leading 30-26, Lavender hit a short jumper in the lane made possible by Sarah Schulze, who tapped a Prahalis miss to the All-America center in the middle of the lane for an easy conversion.
The next time down, Schulze hit the boards again and followed another Prahalis miss with a short basket of her own.
Buckeye Amber Stokes followed with a pair of layups, the first coming after she drove through the heart of the zone and the second when she outran the Cavs down the floor on a fast break.
Lavender finished the half with a short bank shot in the lane on a feed from Prahalis, who started a fast-break with a steal at the top of the key on the other end.
Virginia shot a miserable 28.3 percent (17 for 60) for the game, following a 29.4 percent first half with a 26.9-percent second stanza.
"We got great looks tonight," Virginia head coach Debbie Ryan said. "I told our team we can't expect to win if we miss as many layups and free throws as we did. The coaches can only do so much. The players have to finish."
She felt her team tired late in the first half when the Buckeyes made their run, but Prahalis thought differently.
"I think we caught a rhythm to end the first half," said Prahalis, who scored 14 points and handed out eight assists with three steals. "We were hitting shots and just playing our basketball."
Lavender led all scorers with 23 points and 13 rebounds. Her eighth and final carom of the first half was the 1,116th of her career, setting a new Ohio State career record held by Tracey Hall since 1988, but all that was on her mind was getting a victory.
"I don't think about stuff like that," she said. "I just rebound."
She was happy to break through in the ACC/Big Ten Challenge, a yearly event in which the Buckeyes lost the first three seasons.
"I think it's really important for us to win this challenge because the ACC has a tendency to think the Big Ten teams can't contend with them, and I pretty much root for all the Big Ten teams to win this challenge just to prove we have the caliber of players to win these challenges," Lavender said.
Simone Eqwu led Virginia with 11 points while Gerson had 10.
The game was staged at St. John Arena in anticipation of Ohio State hosting the first and second rounds of the NCAA tournament in March. A host school must play at least one game at the tournament site during the regular season.