Washington (13-8, 5-3 Pac-12) trailed by 12 points with 18 minutes to go before taking control with a big run midway through the second half. The Huskies led by 11 with less than four minutes to play, but Oregon State (11-8, 3-4) cut it to 78-75 with a minute to go.
Williams-Goss put the game mostly out of reach when he converted a three-point play after being fouled on a drive with 44.8 seconds left, and Washington closed the game by making six free throws in the final 32 seconds.
Wilcox passed the 1,700 career-point milestone and moved into No. 7 on the school's all-time scoring list despite being held in check by OSU's defense most of the game.
Washington coach Lorenzo Romar also had a milestone night, as he earned his 250th win as coach of the Huskies.
Nelson came into the game as the Pac-12's top scorer with 21.7 points a game, and Wilcox was No. 2 at 19.9. In the battle between the two, Nelson held the upper hand except during the Huskies' crucial run.
Nelson had seven points before Wilcox got off his first shot more than 10 minutes into the game, and Wilcox didn't score until four minutes later. At halftime Nelson had scored 15 of OSU's 38 points and Wilcox managed just four, spending the final minutes of the half on the bench after picking up his second foul.
With NBA Hall of Famer Bill Russell watching courtside, Wilcox -- and the Huskies -- got off to a slow start again in the second half. The Beavers scored the first seven points of the half to take their largest lead of the game, 45-33.
Washington had cut the lead to six with 14 minutes to go, and then quickly turned the deficit into a double-digit advantage.
The Huskies went on a 14-2 run -- including Wilcox's first eight points of the half -- to go ahead 59-55, and pushed the lead to 10 points, 68-58, with seven minutes left in the half.
The loss snapped a two-game winning streak for the Beavers, who haven't beat UW in Seattle since 2003.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.