The win was the 17th in which Washington (5-1, 3-1 Pac-10) has rallied in the fourth quarter in 22 games under coach Rick Neuheisel. The Huskies staged fourth-quarter comebacks earlier this season against Michigan, California and Southern California.
Pickett overcame four interceptions and completed 29 of 49 passes for a school-record 455 yards and two touchdowns. He surpassed Cary Conklin's 428 yards against Arizona State in a 34-32 loss on Nov. 4, 1989.
Pickett returned to the lineup after missing last week's 35-13 loss at UCLA with a right shoulder injury.
Arizona (3-4, 0-4) took its first lead, 28-21, on Clarence Farmer's 16-yard touchdown run with 5:19 remaining. But Washington intercepted Wildcats quarterback John Rattay to set up a 39-yard field goal by John Anderson with just over four minutes left to slice the deficit to four points.
Farmer carried 21 times for 147 yards, but Arizona suffered a blow when starting quarterback Jason Johnson left with a concussion late in the first half. Johnson completed seven of 10 passes for 80 yards and two touchdowns before leaving.
Washington owned a 21-14 lead after a wild opening 15 minutes. The Huskies posted their 12th straight home victory.