The Mustangs (2-1) had the first drive of overtime. But Bo Levi Mitchell threw deep into the end zone on the first play and was picked off by Chima Nwachukwu. It was Washington State's fourth interception of the game.
The Cougars (1-2) took over on the 25 and gained just three yards on three plays before Grasu's game winner. Earlier in the game he missed a 39-yard field goal.
It was the first time Washington State had led all season.
Southern Methodist led 24-7 in the third quarter and seemed to be cruising to victory.
Then the WSU defense took control.
Linebacker Alex Hoffman-Ellis picked off Mitchell at midfield and ran the ball back 52 yards for a touchdown late in the third. But the snap for the conversion was fumbled, and the Cougars trailed 24-13. That missed extra point would end up costing them a chance to win in regulation.
Matt Szymanski kicked a field goal early in the fourth for SMU.
Linebacker Myron Beck picked off a scrambling Mitchell and outran the Mustangs for a 67-yard touchdown that cut SMU's lead to 27-20 with 10:07 left.
Mitchell led SMU deep into WSU territory on the next drive but was picked off by Brandon Jones. The Cougars' offense went 3-and-out, but SMU did the same and Washington State got the ball back on its 20 for one last drive.
The Cougars benefited from a key pass interference call on fourth down against Sterling Moore on receiver Jared Karstetter that gave them first down on SMU's 34. Quarterback Marshall Lobbestael completed two passes to give them first down on the SMU 7 with 36 seconds left.
On the second play, Lobbestael hit a diving Karstetter in the end zone with 28 seconds left. Grasu kicked the extra point to tie the game at 27-27.
The loss ruined a career day for Mitchell, who completed 40 of 57 passes for 424 yards and two touchdowns, but also four interceptions. Receiver Emmanuel Sanders caught a school record 18 passes for 178 yards, while Terrance Wilkerson caught two touchdown passes.
The Mustangs had 504 yards of offense, compared to 276 for WSU.
Lobbestael, who replaced Kevin Lopina at starting quarterback this game, completed 24 of 52 passes for 239 yards and was picked off twice. Karstetter finished with five catches for 63 yards.