Washington won the league's regular-season title with a 14-4 conference record, but fell behind by 13 points in the tournament quarterfinals and was unable to make the plays down the stretch.
Cunningham scored a go-ahead layup with 30 seconds to go and then hit two free throws with 6.2 seconds remaining. He scored 28 points to go with 10 rebounds and eight assists.
Oregon State (19-13), which came into the event as the No. 9 seed, got past Oregon State Wednesday in the opening round. The Beavers will face fourth-seeded Arizona in Friday's semifinals after the Wildcats eliminated UCLA 66-58.
California advanced with a 77-71 decision over Stanford and will meet Colorado in the other semifinal after the Buffaloes won a 63-62 thriller over Oregon.
Washington was led by Tony Wroten, who set a school freshman single-game record with 29 points.
Arizona reached the semifinals thanks to a 25-point performance from Solomon Hill. The Wildcats (22-10) pulled away late after the game had been tied with 6:30 to play.
Arizona made 31-of-36 free throws while UCLA connected on just 10-of-16. The Bruins (19-14) were paced by Lazeric Jones with 17 points.
California poured in 54 points in the second half to overcome a seven-point halftime deficit. Jorge Gutierrez led the Golden Bears (24-8) with 22 points.
Andrew Zimmerman had 22 for Stanford (21-11), which was even with California with 4:53 to go in the game before the Golden Bears ran off eight straight points.
Colorado downed Oregon thanks to an offensive rebound and layup by Andre Roberson with 13 seconds to play. The Buffaloes then survived a last-second, 3-point miss by Devoe Joseph.
Carlon Brown led Colorado (21-11) with 18 points. The Ducks (22-9), who got 14 points from Tony Woods, made just 4-of-21 from 3-point range.