Utah (17-9, 9-6 Pac-12) used a 17-0 run -- as the Cougars were scoreless for six-plus minutes -- to make it 33-13 with nearly six minutes left in the first half before taking a 10-point lead into the break.
Rawson, who hit six 3s and scored 22 points for the Utes in their last meeting with Washington State (10-16, 2-12 Pac-12), made 3 of 4 from 3-point range, scored 11 points and grabbed seven rebounds in the first half on Saturday.
The Utes scored the first seven second-half points and Utah held on from there.
"We are understanding (that) when you play defense, you can be in a lot of games," Utah coach Larry Krystkowiak said.
WSU threatened several times, cutting its deficit to four with 2:13 to play after Viont'e Daniels hit back-to-back 3's in a 30-second span. Bibbins answered with an acrobatic jumper in the lane and, after Daniels made a layup, hit two free throws to make it 76-70 with 14 seconds left.
"Viont'e's bucket was a late game play. We haven't run that play in four years," WSU coach Ernie Kent said. We practice it enough and you just keep it in your back pocket until you need it".
Gabe Bealer scored 18 points on a career-high tying six 3s for Utah.
Malachi Flynn, who had a career-best 30 points in WSU's win over Colorado on Thursday, scored 20 with four steals against the Utes. Robert Franks added 18 points with seven rebounds and Daniels scored 14, hitting 4 of 8 from behind the arc.
We really, really played hard in the game, and we tend to have that piece figured out," Kent said. "I don't think we played very smart in the game."
Utah: The Utes have won four in a row and will head back home to play a tough UCLA team. Utah is currently fourth in the conference standings with three regular-season games to go. The top four teams get a first-round bye in Pac-12 Tournament.
Washington State: After a comeback win against Colorado, the Cougars suffered their 16th loss in the last 20 games. WSU started the season 6-0, including a win over San Diego State in the Wooden Legacy championship.
Utah: The Utes play UCLA at home next Thursday.
Washington State: The Cougars go for a season sweep over California, in Berkeley, on Thursday.
Crosby, Howard give Alcorn State 74-69 win over Pine Bluff
Troymain Crosby scored 20 points with eight rebounds and Maurice Howard made four free throws in the final 20 seconds as Alcorn State held off Arkansas Pine Bluff 74-69 on Monday night.
Mason scores 29, Baylor defeats West Virginia 85-73
Makai Mason scored 29 points and Baylor cruised to an 85-73 win over West Virginia on Monday night.
Williams: 'I got a better sense of humor' than Belichick
When Roy Williams is asked about the success his team had tonight, he has a hilarious answer that includes mention of Bill Belichick.