PULLMAN, Wash. -- Washington State receiver Gabe Marks doesn't think becoming bowl-eligible is that big a deal.

Washington State came from behind to beat Arizona State 38-24 on Saturday for its sixth victory of the season.

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"I don't think it's very significant," Marks said. "We've played good enough to get to this point. But we don't want to be satisfied with just being bowl-eligible."

Washington State coach Mike Leach agreed the Cougars have a lot to accomplish in their remaining three games. They need to win a seventh game to be guaranteed of going to a bowl, Leach said.

"We haven't reached our potential," Leach said.

Washington State fell behind 14-0 early, but came back to score 21 points in the fourth quarter to seal the win.

"As a team, we finished this game better than any game all year," Leach said. "This game was on the bubble and we put it out of reach."

Luke Falk threw for 497 yards and five touchdowns for Washington State (6-3, 4-2 Pac-12), while Dom Williams caught six passes for 123 yards and two touchdowns.

Arizona State (4-5, 2-4) scored a touchdown on each of its first two possessions, then was held to one more the rest of the game. It was the Sun Devils' third consecutive loss.

"This is a disappointing, disappointing season," Arizona State coach Todd Graham said. "Ultimately, I'm responsible for it."

Washington State, which lost on a last-second missed field goal last week against No. 9 Stanford, managed to protect Falk from one of the best pass rushes in the Pac-12. He completed 36 of 55 passes, with one interception, and was sacked three times.

Arizona State quarterback Mike Bercovici completed 27 of 44 passes for 229 yards. The Sun Devils did get 111 rushing yards from Demario Richard and 84 from Kalen Ballage.

Jamal Morrow, Keith Harrington and John Thompson each caught touchdown passes for Washington State.

Arizona State scored on its opening drive, with Richard running into the end zone from the 6-yard line. Richard had runs of 26 and 15 yards during the 70-yard drive.

Ballage scored on a 9-yard run on Arizona State's second series, capping a 64-yard drive, for a 14-0 lead midway through the first quarter.

Falk was intercepted by Kareem Orr on the first play of the ensuing series, giving the Sun Devils the ball at WSU's 22. Bercovici tried to run in on fourth down from the 3-yard line and was tackled for no gain, turning the ball over on downs.

"That was pretty important," Graham said.

Washington State took over and marched 92 yards down to the 5-yard line, where the drive stalled. Erik Powell kicked a 22-yard field goal to put the Cougars on the scoreboard.

On the next series, Marcellus Pippins recovered an Arizona State fumble at WSU's 32, but the Cougars had to punt.

The Cougars got the ball back at the Arizona State 16 on a 38-yard punt return by Gabe Marks. Washington State failed to convert on fourth-and-5, but got a second chance on an inadvertent whistle by a game official. Falk then threw an 11-yard touchdown pass to Williams to cut Arizona State's lead to 14-10 at halftime.

Marks said he heard a faint whistle during the play and turned to the official.

"I was like: `Dude, why?'" Marks said.

Graham said the inadvertent whistle was "pretty big," but declined to comment further.

Falk threw a 23-yard touchdown pass to Harrington on WSU's first drive of the second half, lifting the Cougars to their first lead at 17-14. The drive covered 94 yards in nine plays.

Arizona State used a trick play on fourth-and-12 to keep its next drive alive. Punter Matt Haack threw a pass to a wide open D.J. Foster for a 27-yard gain, giving the Sun Devils first down on the WSU 13. Bercovici ran over from the 1 to lift the Sun Devils to a 21-17 lead late in the third.

Washington State replied with a 73-yard drive, kept alive by a 16-yard pass reception by Marks on fourth-and-1. Thompson caught an 8-yard touchdown pass from Falk to put the Cougars up 24-21 with 13 minutes left in the game.

After an ASU punt pinned them on the 1-yard line, Washington State drove 99 yards, with Falk throwing the final 12 to Morrow for a touchdown. That put the Cougars ahead 31-21 with 8 minutes left.

Zane Gonzalez kicked a 22-yard field goal with 4:13 left to cut Washington State's lead to 31-24.

The Cougars replied with a 75-yard touchdown pass from Falk to Williams on the first play of the ensuing possession for a 38-24 lead.

Arizona State was coming off a 61-55 triple overtime loss to Oregon.

Falk is averaging more than 400 yards per game through the air, and the Cougars lead the Pac-12 in passing yardage.

The Sun Devils rank second in the nation with 9.5 tackles for loss per game. They lead the Pac-12 in sacks this season.

Arizona State's D.J. Foster has caught a pass in 49 consecutive games, breaking the Pac-12 record.