The next time down the floor, Shavelle Little was the thief, and she found Prahalis who outraced the Boilermakers to the other end for a layup and a three-point advantage.
Danielle Campbell hit two free throws for Purdue to temporarily stem the tide, then Ohio State scored the next six.
Lavender made a putback then Prahalis had another breakway layup before Allen capped the run with a pair of free throws to set the score at 35-26 with 14:53 to go.
The Boilermakers (15-8, 8-4) nearly caught the Buckeyes (19-3, 10-1) five minutes later, but 39-38 was as close as they would get.
With 6:26 left to go, Prahalis made a three-pointer to double Ohio State's lead to 48-42, and when teammate Maria Moeller added another trey 1:15 later, the game was essentially over.
That Prahalis and Moeller were open was just what Purdue coach Sharon Versyp had planned, an idea that worked up to that point as a collapsing zone defense worked to slow Lavender and Allen with varying success.
The Buckeyes' halfcourt offense was stuck in neutral for much of the night, especially the first 20 minutes when they shot a dreadful 30.8 percent (8 for 26).
Fortunately for the hosts, their defense was nearly as good as their offense was not.
They held Purdue to 33.3-percent shooting (10 for 30) in the opening half and scarcely let up. When all was said and done, the Boilermakers were 18 for 53 from the field, an even 34.0 percent.
Ohio State shot 51.9 percent in the second half, making 14 of 27 shots. They never really warmed up from the perimeter but were able to get out on the break for a few easy ones and to manufacture others in the halfcourt to pull out the win.
The head coach of the Buckeyes, Jim Foster, attributed the improvement to a better energy level.
"I thought we played good defense in the first half, but I didn't think our transition to the other end of the floor was that good," he said. "In the second half, it got better."
He acknowledged having a stern message for his players in the locker room at halftime, but by the end of the game, he was in a joking mood.
"We scored 25 points on turnovers and they scored seven," Foster said. "That says a couple things. Some of our turnovers were so bad we were throwing the ball in the bleachers. You can't run on them."
Prahalis struggled more than the rest as the highly touted recruit missed her first eight attempts from beyond the arc and 10 of 11 for the game. She scored 11 points and was charged with eight turnovers but found ways to make enough plays to get her team ahead and keep it there.
After the game, she admitted feeling relieved to see the ball finally go through the net after casting off from beyond the arc with the game still in doubt.
"I mean, my shot has been off for a while, but I've just got to keep shooting and keep practicing," she said. "That's probably the main thing. Keep getting reps before practice and hopefully one of these games I'll be back on."
Her coach pointed to the fact she helped hold the starting Purdue backcourt of Jodi Howell and Lauren Mioton to 0 for 8 shooting and one total point.
"I think this team just plays solid defense and takes responsibility for the individual matchups," Foster said. "Sammy struggled a little bit shooting the ball and then she's guarding someone who didn't get a field goal. She doesn't dwell on that, and that's one of the things I like about her. She doesn't dwell it. She doesn't say, ‘OK, I'm not making shots, therefore I'm going to pout when I get down at this end.' No, she goes down and makes sure that if she's not putting them in the basket, neither is that kid, and I think that makes a big difference."
Doing the majority of the damage for the Buckeyes was the inside duo of Lavender (19 points) and Allen (14).
Lindsay Wisdom-Hylton led Purdue with 20 points, including 12 in the first half.
Foster credited Lavender for making her life more difficult in the latter 20 minutes. Such an effort came on a night she broke the 1,000-point barrier, becoming the second-fastest Buckeye to do so. While Katie Smith reached the milestone in her 52nd game, Lavender did so in her 53rd.
Her coach said the evening was a good example of the type of player she is and the expectations she now faces.
"She had a good first half, but the bar has been raised with Jantel," he said. "If you want to be a great player, there are great challenges that come at you. In the first half I don't think she was as aggressive as she is capable of being. In the second half, I think she was terrific defensively. You just challenge good players and they respond. They want to be coached and they want to get better. That's one of the things Jantel brings to the gym on a daily basis. She plays hard and she wants to get better."
Lavender, of course, downplayed the accomplishment.
"It was just something fun," she said, noting that it gave her teammates something to tease her about as the big round number approached. "They were playing around with it, but I wasn't looking up at the scoreboard counting."
"I think it's great," Allen chimed in with a big smile. "She worked hard for it to get that thousand. She's a great player."
With the win, Ohio State swept the season series and pushed the Boilermakers three games back in the loss column in the Big Ten standings.