Washington (13-18) appeared to be headed toward a rout, but blew a 15-point lead with 8 1/2 minutes left.
The sixth-seeded Huskies went 8 minutes without a field goal as Washington State (17-15) scored 15 straight points to tie it. Desmond Simmons put Washington up by two with a tough shot inside with 1:16 remaining, and Washington State's Brock Motum badly missed a 3-pointer while trying to draw a foul with 3 seconds left.
Abdul Gaddy had 11 assists for Washington, which moves on to face third-seeded Oregon in Thursday's quarterfinals.
Motum had 28 points in what's likely his final game for Washington State, and D.J. Shelton added 19.
Washington came into the tournament after a regular season filled with streaks.
The Huskies opened Pac-12 play with four straight wins, lost seven of eight, then closed the season 3-1. Washington finished tied for sixth in the conference 9-9 and was likely looking at a Pac-12 title as its only shot at making the NCAA tournament.
The Huskies fell flat at last year's tournament, losing to Utah in the opening round to become the first team from a power conference to win the regular season title and not make the NCAA tournament.
Washington State went through a tough regular season, losing games to ranked teams like Kansas and Gonzaga before laboring 4-14 through the Pac-12. The Cougars did end the season on an uptick, beating then-No. 23 UCLA by 12 and completing the Southern California sweep by blowing out USC by 25.
Washington swept two meetings between the rivals during the regular season, but both games were close: by five in Spokane on Jan. 5 and by four 10 days earlier in Seattle.
The Huskies jumped on the Cougars early in the 277th meeting between the schools, hitting five of their first nine shots and using an 11-0 run to go up 15-5.
After going more than 7 minutes without a field goal, Washington State started hitting shots, but had a hard time trimming that initial deficit.
Suggs had 13 points by halftime, and Washington led 36-25.
The Huskies opened the second half with a pair of alley-oops by Gaddy and kept flying, going up 48-31 on consecutive 3-pointers in the corner by Wilcox.
Washington State fought back with the 15-0 run, capped by consecutive layups by Royce Woolridge that tied the game at 62 with just under 3 minutes left.
Simmons answered with his shot inside, and Washington State failed on two possessions while trying to tie, fumbling the ball away before Motum's last-second shot was off the mark.