Poyer's second interception forced Halliday from the game. His third, with 3:18 remaining, sealed the victory.
"It was the biggest performance," said Oregon State defensive end Scott Crichton, who added three sacks. "That's a superstar right there. He carried us."
The Beavers (4-0, 3-0 Pac-12) needed the defensive effort, as the offense -- and quarterback Sean Mannion -- struggled.
Mannion threw three interceptions and finished 25 of 42 for 270 yards. He was sacked three times.
Markus Wheaton had 95 yards receiving and a touchdown. Oregon State has surpassed its win total for the 2011 season and is 4-0 for the first time since 2002.
Tuel was 11 of 17 for 126 yards after replacing Halliday, who threw three interceptions.
Marquess Wilson had four catches for 54 yards to lead the Cougars (2-4, 0-3). Halliday was 9 for 20 for 81 yards.
Turnovers hurt the Cougars as they continue to implement new coach Mike Leach's pass-heavy offense.
Crichton and sophomore defensive end Dylan Wynn kept both Halliday and Tuel on the run. All together, the Cougars had four interceptions and a fumble.
"(The Beavers) were jumping routes because they were playing a lot of man coverage," Tuel said. "They were playing it tight, and honestly, it's just a small place to throw a football."
Mannion was selected the Pac-12 offensive player of the week after throwing for 433 yards last week in a 38-35 win over Arizona. But he was not sharp to start Saturday's game, missing receivers and throwing two interceptions early.
The Beavers had another promising drive stopped when they failed to convert a fourth-and-2 at the Washington State 24. Oregon State had to settle for Trevor Romaine's two field goals and a 6-3 halftime lead.
Mannion showed more poise in the second half. He led the Beavers down the field for a 75-yard scoring drive to start the third quarter, hitting Wheaton for a 12-yard touchdown pass.
"I'm really proud of the way our team came out in the second half," Mannion said. "I think that says a lot about us."
In the fourth quarter, Mannion led a 13-play, 86-yard drive that Tyler Anderson capped with a 1-yard run. The Beavers were 3 for 3 on third downs during the drive.
"And two of those third-down conversions were major league," said Oregon State coach Mike Riley, who became the school's winningest coach in last week's win at Arizona.
Helped out by two 15-yard Oregon State penalties, Tuel completed 5-of-7 passes on a drive early in the fourth, but it ended in Andrew Forney's 32-yard field goal.
"I thought we were pretty disjointed on offense," Leach said. "Oregon State's defense was more physical than our offense."
Top 25 Overview
It was over when... Wazzu pulled within 7 of Oregon State in the 4th, but the Beavers came right back with a TD and a subsequent INT to put it away.
Gameball goes to... CB Jordan Poyer intercepted Washington State QB Jeff Tuel three times for 52 yards. Tuel was picked off four times total.
Stat of the game... 4-0. Oregon State is 4-0 for the first time since 2009. Coincidentally, that fourth 2009 win came against Wazzu.