WEST LAFAYETTE, Ind. -- For four seasons, Purdue senior guard Rapheal Davis has embodied a Boilermakers basketball program that has relied on physical and mental toughness since Gene Keady coached in West Lafayette, now followed by Keady protege Matt Painter.

While Davis, who scored 19 first-half points, was 1 of 12 from the field in the second half and overtime Tuesday night, he was the player asked to win the game in the closing seconds.

Davis made one of two free throws with 4.6 seconds remaining in overtime, and No. 18 Purdue defeated No. 8 Michigan State 82-81 in Mackey Arena.

Davis, who finished with 24 points and seven rebounds, missed the second free throw, but Boilermakers center A.J. Hammons grabbed the rebound as time ran out. Hammons had 19 points, 13 rebounds and eight blocks.

"Even though I was 1 of 12, coach had the trust in me at the end," said Davis, who hadn't beaten Michigan State until Tuesday. "To make that (free throw) to win the game, that's something you dream of as a kid."

Spartans guard Denzel Valentine, who led all players with 27 points and 10 assists, tied the game on a driving layup with 11.5 seconds to go in overtime but fouled Davis after a Purdue timeout.

"We wanted to get the ball inside on that last play," Painter said of what was discussed during the timeout with 6.7 seconds to go. "We wanted to get the ball to Ray and have him turn the corner with A.J. following him to the rim. I told Ray to grind it.

"Ray played a great first half and overtime, but he lost his mind in the second half, taking a bunch of off balance Dwyane Wade runners. But Ray always has been about us winning, and that is what he did. Had we lost this one, it would have been devastating."

Purdue, which beat a top 10 team for the first time in five years, improved to 20-5, 8-4 in the Big Ten.

The Spartans (20-5, 7-5) rallied from a 16-point halftime deficit to force overtime but could not overcome the Boilermakers in the extra session.

Purdue forward Caleb Swanigan missed a 3-pointer, Hammons missed a turnaround and Valentine missed a jumper in the final 12 seconds of regulation to force overtime with the score tied at 72.

"We played hard, but we didn't play smart," Michigan State coach Tom Izzo said. "It's especially tough when you miss three dunks and lose by one point. Matt had his guys ready to play. Their big guys are hard to guard. I thought the better team won tonight."

Purdue scored the first four points in overtime, but Michigan State, which got 11 points from Matt Costello and 10 from reserve guard Matt McQuaid, fought back to tie it at 81 before Davis' free throw won it, and Hammons key offensive rebound saved it.

"I just reached in there and wasn't going to let that rebound get away," Hammons said. "I'm very proud of Ray. He played a great game."

Michigan State used a 7-1 run, capped by a Valentine layup, to take a 70-66 lead with 4:27 remaining in the second half. Two Hammons free throws with 3:31 to go pulled Purdue within 70-68.

Two free throws from forward Kenny Goins extended the Spartans' lead to 72-68 with 1:59 to go before a Swanigan layup closed the gap to 72-70.

Swanigan's layup tied it at 72 with 1:04 to go.

Costello's layup with 7:40 remaining gave Michigan State its first lead, 61-60. At that point, Purdue was 5-for-22 from the field in the second half.

The Spartans, meanwhile, made five of their first seven 3-pointers after halftime.

A 3-pointer from guard Alvin Ellis, three Ellis free throws and a layup by guard Matt McQuaid pulled the Spartans within 56-55 with 10:03 to play.

Hammons' three-point play gave Purdue's 59-55 lead, but a Costello layup and a dunk by forward Deyonta Davis tied it at 59 with 8:43 remaining.

Michigan State opened the second half on a 14-4 run, including three consecutive 3-pointers from Valentine, pulling to within 50-44 with 16:06 to play.

Purdue reserve point guard Johnny Hill scored six points during the final 1:58 of the half, helping the Boilermakers lead 46-30 in what collectively was their best first half of the season.

NOTES: Since 1995-96, Michigan State G Denzel Valentine is the only Division I player to average at least 17 points, seven rebounds and six assists in a season. ... The Spartans entered ranked fourth nationally in both 3-point field goal percentage and 3-point field goal percentage defense. ... Michigan State came in having beaten Purdue seven consecutive times, beginning with a 74-56 victory on March 11, 2011, in the Big Ten tournament. ... Three of Purdue's five losses have been administered by No.

4 Iowa (twice) and No. 2 Maryland. ... The Boilermakers earned their first victory against a top 10 opponent since defeating then-No. 2 Ohio State on Feb. 2, 2011 in Mackey Arena. ... Purdue is 14-1 at home this season, losing only to No. 4 Iowa on Jan. 2.