To open the second half, Syracuse guard Erica Morrow made a layup to cut the OSU lead to 34-30, but 17th-ranked Ohio State scored 11 of the next 13 points.
Four different Buckeyes scored during the spurt.
She was open after the Orange's 2-3 zone defense collapsed on Jantel Lavender in the post.
On Ohio State's next possession, Johnson made the defense pay for closing out on her by finding Star Allen under the basket for an easy layup that put the Buckeyes ahead 42-30.
After Chandrea Jones scored for Syracuse, Prahalis brought the fans to their feet with a nifty pass to Lavender in the lane on the fast break. Ohio State's center collected the ball and made a layup on the move. She also drew a foul and brought the fans to their feet.
She made the ensuing free throw to complete the play and put Ohio State ahead 45-32.
The Buckeyes (3-0) led by as many as 16 later in the game, but the Orange (2-1) would not go away.
They scrapped their way back a couple of times with aggressive defense and an opportunistic fast break attack.
They cut the lead to seven twice, first on a layup by Morrow with 6:56 to play and then again when Morrow made a trey with 0:23 left, but that was as close as they would get.
Ohio State's Alison Jackson answered the layup with a three-pointer and then Prahalis made a 12-foot jump shot to push the lead back to 12.
Morrow led all scorers with 23 points, but she needed 28 shots to hit that total. She made 10 field goals, including 2 of 7 threes, and added five rebounds.
Lavender paced Ohio State with 22 points while Prahalis scored 17 and Johnson pitched in a crucial 15.
"I'll tell you what, Brittany Johnson really won the game for them," Syracuse coach Quentin Hillsman said. "Because our thing was to force them to shoot the perimeter shot and she came out and took the challenge. She didn't hesitate as much as we thought she would on the perimeter. We were more worried about her driving or throwing the ball inside, but she took a couple strong, strong shots, and when you've got a kid that gets it going like that it gets your kids second-guessing if they should go out on her. But we just stayed solid and said, ‘Hey, if she's going to shoot 12 threes, I feel good about that.' "
Johnson made 4 of 12 threes and 5 of 15 field goals overall, while Lavender, the reigning Big Ten co-player of the year, saw her touches limited.
"Jantel only had 11 attempts for the whole game, so I thought we did a pretty good job, but she made nine of them, so it's tough," Hillsman said.
Playing with Lavender, who had her 16th double-double of her relatively short career, means players like Johnson know they will get their opportunities.
"I was more comfortable," she said. "We've never really seen a zone before. No one has ever really played a zone against us. So, like Coach (Jim) Foster said, we always have to be ready and I think that I was ready tonight. I had my feet set and I knew that Jantel was being doubled so she was going to kick the ball out to me so I was ready for it.
Foster was happy with how his team reacted against the Orange zone and is looking for his team, with three first-year starters and just one senior, to continue to improve as the season goes on.
That includes Johnson.
"I think quite frankly she's going to shoot the ball a heck of a lot better through the course of the year," Foster said. "She can shoot the ball even better than she shot it tonight. We think she's going to be a very good basketball player."
Juanita Ward added 11 points and 12 rebounds for the Orange, who returned four starters from a team that went 22-9 and made the NCAA tournament last season. Jones had 14 points five steals.
"When you play against teams of that level of talent that play in a conference that they go into big arenas and play very good teams and they know what they're doing," Foster said. "We sent a very, very young team out there and I think they handled themselves very well. The last three minutes, we need to get better at that and we will."