As a senior, Parrish was named a team captain and led the huskies to an 8-4 record; he was also second-team All-Pac-10 and a semifinalist for the Jim Thorpe Award. He recorded 81 tackles, six interceptions (team-leading), four passes defended, two forced fumbles, two fumble recoveries, and two touchdowns. In the Aloha Bowl that year, the Huskies beat Michigan State 51-23, a game that included Parrish returning an interception 56 yards for a touchdown. While Parrish played for the University of Washington, the Huskies recorded a 31-15 overall record, along with a 22-9-1 record in the Pacific-10 Conference. From 1994-1997, Parrish played in 46 of the 47 games he was eligible to play in during his career at the University of Washington.