The Huskies (2-1) notched their 16th consecutive home victory and handed the Cowboys (0-4) a school-record 12th straight defeat.
Washington took a 10-7 lead on a 21-yard field goal by John Anderson with 9:15 to play in the second quarter. Just over five minutes later, Rich Alexis scored on a one-yard run to give the Huskies a 10-point advantage at the half.
The Huskies put the game away in the third quarter. Alexis posted another one-yard touchdown with 10:40 to go in the period and Paul Arnold made it 31-7 with a 10-yard catch from Pickett with 4:02 remaining in the period.
Pickett's eight-yard pass to Patrick Reddick with 12:28 to play concluded the scoring. An Idaho native who was named by his rodeo-champion father, Pickett completed 34-of-45 pass attempts without an interception.
Wyoming quarterback Casey Bramlet, was 20-of-31 for 186 yards with one interception. He was sacked six times.
Alexis ran for 94 yards while sophomore Reggie Williams caught six passes for 100 yards.