TUCSON, Ariz. -- It was a game Rich Rodriguez termed "redemption and relevancy" as Arizona prepared for No. 15 Washington State. It was the last thing he told his team before it faced the Cougars.

It worked out well for host Arizona, which won 58-37 in its homecoming game at Arizona Stadium on Saturday night.

Arizona avenged last season's 69-7 loss to Washington State in Pullman, Wash., in what Rodriguez called a "debacle."

"It was a chance to be relevant if you beat a top 25 team and they were 15th and that gives you a chance to be relevant for a little bit," Rodriguez said after the win. "I know they want to be bowl eligible but the more you win the more that is at stake."

Arizona (6-2, 4-1 Pac-12) remained in the thick of the Pac-12 South race, and faces No. 21 USC (7-2, 5-1) in Los Angeles next week.

"We're going to have to play better," Rodriguez said about next week. "We know we are capable. Our guys know we have to do that next Saturday."

Washington State (7-2, 4-2) entered the game with the nation's fifth-best passing game, and passed for 602 yards Saturday.

It came down to Arizona's strength -- the running game. Behind quarterback Khalil Tate and J.J. Taylor, the duo helped Arizona collect 310 yards on the ground.

Taylor, a redshirt freshman, rushed for 152 yards and two touchdowns. Tate ran for 146 yards, including an 82-yard run, and passed for 275 yards and two touchdowns.

"They stopped the run (early) and it opened up (the pass)," said Tate of Washington State's strategy. "It was a lose-lose situation."

It was the breakout game Rodriguez had been expecting from Taylor.

"I've kind of waited, but they did a great job up front," Rodriguez said. "I don't know if anyone has run that well on them but (we) went at it."

Arizona's went into the game as the nation's fourth best running attack, averaging 342.3 yards per game. The Wildcats, who ranked No. 7 in the nation in total offense (514 yards per game), had 585 total yards.

Starting Washington State quarterback Luke Falk was replaced late in the second quarter and didn't return. His backup, Tyler Hilinski, had some success and at one point gave the Cougars the lead 27-23 in the third quarter. But he threw four interceptions, and one of those picks was returned 66 yards for a fourth-quarter touchdown by Colin Schooler that made the score 50-30.

"I wanted (Luke) Falk to see the field because we weren't pushing the ball down the field," WSU coach Mike Leach said of the switch. "Then, (Tyler) Hilinski was hot, so we stayed with Hilinski. I think Hilinski does a good job of bouncing around and pushing the ball down the field, but he gets reckless. ... We played dumb against a really good team."

Hilinski went 45 for 61 passing and two touchdowns. WSU had 646 yards in total offense.

He threw a 49-yard touchdown to Tay Martin with 9:46 left to give WSU a chance late, making it 51-37. But Arizona added another touchdown to make it 58-37.

The two teams combined for 58 points in the second half with Arizona outscoring the Cougars 35-23.

It was a game Arizona had to remain patient on offense.

"They can make you look ugly," Rodriguez said. "They are active upfront with all their movements. You have to stay patient. We did a couple of play-action passes and I thought that was the key. That still didn't loosen them up (on defense), but it got us some big plays and kept us in the game."

After WSU took a lead 27-23 early in the third quarter, Arizona regained the lead with 7:35 left in the third quarter when Taylor scored on a 3-yard touchdown run after he ran 62 yards to get to the 3.

That put the Wildcats ahead 30-27, and the Cougars never led again.

"We were moving the ball down the field and we just couldn't make the plays when we needed to," said running back Jamal Morrow.

Arizona's Taylor broke loose for a 79-yard touchdown run to give UA a 37-27 lead with 2:53 left in the third quarter.

After a Washington State field goal, Tate scored on Arizona's next possession to give the Wildcats a 44-30 lead with 12:50 left.

"I thought they played hard but dumb," Leach said. "I thought we played extremely hard. But they had big plays and we got frantic, which meant we played harder and out of position.

"We played hyper aggressive and tried to do too much."

The first half ended with Arizona holding a nine-point lead.

Arizona freshman kicker Lucas Havrisik booted a 57-yard field goal to end the half and give Arizona a 23-14 lead over Washington State. The kick came with no time left on the clock.

In Washington State's previous possession, Hilinksi rushed for a 6-yard touchdown with 10 seconds left in the half to help WSU reduce Arizona's lead to 20-14.

Falk, who had thrown 22 touchdown passes this season entering the game, was replaced late in the first half by Hilinski. Falk had thrown a 1-yard touchdown pass earlier in the game.

He finished 13 of 23 for 91 yards, one touchdown and no interceptions.

Tate had a run of more than 70 yards for the fourth consecutive game. He had an 82-yard run late in the second quarter that set up a 25-yard field goal to make it 20-7 with 2:56 left in the half.

NOTES: Washington State QB Luke Falk threw for one touchdown, going 13 for 23 before being replaced in the second quarter. ... Arizona freshman LB Colin Schooler, who broke up the pass to help the Wildcats beat California last week, ran back an interception 66 yards for a TD. ... Arizona played without senior RB Nick Wilson (ankle). ... Tate's 275 passing yards were a career high. ... Washington State had 101 plays to Arizona's 51.