The senior point guard put No. 10 Ohio State ahead for good when she picked up a loose ball and outraced two Purdue defenders to the other end for a layup that made it 67-65 with 4:04 to go.
The Buckeyes (22-3, 9-3) were still clinging to that two-point lead in the final minute when Prahalis inbounded the ball to center Ashley Adams, who immediately kicked it back out to her for a wide-open three-pointer that made it 76-71 and brought a season-high crowd of 8,422 to its feet at Value City Arena.
"I think my girl doubled Tayler so I wouldn't get the pass to Tayler," Prahalis said of the three-point play. "Ashley posted up pretty strong so I passed to her. She made a great pass back and I hit it."
Purdue head coach Sharon Versyp said there was a miscue from one of her players.
"We just made a mistake – a big one – and they were able to knock down a three," she said. "I think them nailing that shot was a big key for them. Our defense, we were supposed to stay on the ball. We never double team. There were other things coming up to it but that's what it comes down to. You have to stay on the basketball."
Prahalis slammed the door seconds later when she stepped into a passing lane to break up a play. She came up with the ball and found teammate Tayler Hill, who was fouled and made a pair of free throws to make it a three-possession game with 24 seconds left.
"It was kind of like a grind it out game," said Prahalis, who had a game-high 26 points on 8-for-16 shooting from the floor. "It was hard for us to get gelling but we grinded it out and played as a team and we won."
She also made 8 of 10 free throws and was one of four Buckeyes to score in double figures, joining Amber Stokes (14), Adams (13) and Hill (12).
The Boilermakers shot 47.5 percent (29 for 61) and dominated the glass (41 rebounds to 24) but were hurt by 18 turnovers.
Ohio State scored 24 points off those miscues to more than offset the 14-11 deficit the Buckeyes faced in second-chance points.
The Buckeyes struggled offensively in the first half and trailed 37-31 after 20 minutes. They opened things up in the second with Prahalis predictably taking charge.
"I think in the second half a lot more ball movement created more open shots," Ohio State head coach Jim Foster said. "The first half Sammy was going sideways. Back it up and now attack. Much better job. Once we started to understand that the flow was better and we were able to get into the lane with different angles."
The Buckeyes beat Purdue (19-6, 9-3) for the fourth straight game.
With the win, Ohio State moved into a virtual tie for first place in the Big Ten with Purdue, Penn State and Nebraska, all of whom have three losses in conference play. Penn State beat Northwestern earlier in the day to become the first 10-win team in the conference this season. The 13th-ranked Cornhuskers (19-4, 8-3). play at Minnesota on Monday night.