Simmons clamped down defensively on Washington State's leading scorer, Brock Motum.
"This was my best game," Simmons said after holding Motum to 15 points on 6-of-13 shooting. Motum averages nearly 20 points per game and most of his points Saturday came late after the Cougars had overcome a big Washington lead.
"The reason we won that game was the tremendous effort on Motum," Washington coach Lorenzo Romar said. "Des did a heck of a job defensively and that put him out of his rhythm."
C.J. Wilcox scored 18 points and Scott Suggs scored three late baskets to help Washington (9-5, 1-0 Pac-12) successfully begin its defense of last year's Pac-12 regular season title.
Mike Ladd scored 15 points to lead Washington State (9-5, 0-1), which has lost four straight to its cross-state rival.
The Huskies jumped to a big early lead and poor shooting plagued Washington State much of the game. The Cougars shot just 36 percent, compared to 54 percent for Washington.
Washington State was scoreless in the first five minutes of the game to fall behind 9-0. Consecutive 3-pointers by Suggs and Wilcox pushed Washington's lead to 17-4 and the Cougars had trouble even attempting shots on several of their possessions.
Shawn Kemp Jr. made back-to-back dunks as Washington built a 21-4 lead and the Cougars were just 2 of 13 from the field at that point.
"We didn't look very in-sync with what we wanted to execute," Washington State coach Ken Bone said. "They did a great job of denying (Motum) the ball."
Washington State rallied for a 13-4 run, capped by Ladd's 3-pointer, which cut Washington's lead to 25-17 with 4:37 left in the first half.
"We hit a couple of shots and got some confidence," Bone said.
Wilcox had 13 points in the first half the Huskies shot 52 percent from the floor. Washington State shot just 27 percent from the field in the first half.
Washington led 34-27 at halftime, and the Cougars scored the first two baskets of the second half to cut the lead to three points, but a 3-pointer by Abdul Gaddy and a basket by Wilcox pushed Washington's lead to 39-31.
Washington State found its range and Ladd's basket cut Washington's lead to 46-42 with 10 minutes left.
Motum's basket tied the score at 48 with 7:54 left, and his 3-pointer less than a minute later gave the Cougars their first lead at 51-50.
The teams swapped leads, with Will DiIorio hitting a pair of 3-pointers for Washington State as the Cougars led 59-58 with 3:10 left.
Suggs' long jumper put Washington up 60-59 with 2:30 left. Motum was fouled on a 3-point attempt and made two free throws for a 61-60 Cougars lead. But Suggs scored on a jumper and a lay-up to give Washington a 64-61 lead with a minute left. Those were the winning points.
Ladd made a pair of free throws and Washington State closed within one at 64-63 with 41 seconds left. The Cougars were forced to foul and Andrew Andrews sank four free throws for the final score.
Romar was pleased with his team's defensive play. "We need an identity on defense, and we showed that tonight," he said.
Aziz N'Diaye added 14 points on 7-of-9 shooting and grabbed 10 rebounds for Washington while Suggs finished with 11 points.
DaVonte Lacy added 10 points for Washington State, which made just 5 of 20 from 3-point range.
"We were not able to put shots down in the game," Bone said. "It didn't go in the basket."
Washington was coming off a loss at Connecticut, but had won its four previous games. The Huskies lead the all-time series 175-100.