Willie Tuitama completed 17 of 21 passes for 193 yards and threw three touchdown passes for the Wildcats (4-1, 2-0), who are looking to end the Pac-10's longest active bowl drought at nine years.
On a breezy night in the desert, Arizona wasted little time putting away the woeful Huskies (0-5, 0-3). Arizona took a 10-0 lead midway through the first quarter when Gronkowski caught a screen pass and raced 37 yards for a touchdown.
Grigsby added a 4-yard run to give Arizona a 17-0 lead after one quarter.
Arizona moved the ball almost at will against the Huskies, who entered with the nation's 114th scoring defense, allowing 40.5 points per game.
Mike Thomas broke the game open with an electrifying 48-yard punt return for a touchdown midway through the second period.
Thomas fielded the ball near midfield, retreated about 10 yards and then cut up the home sideline, sprinting past Washington tacklers. Near the goal line, Thomas leaped over a prone Quinton Richardson and into the end zone as the Arizona Stadium crowd of 55,624 erupted.
The return put Arizona up 24-7 midway through the second quarter, and Gronkowski caught another touchdown pass later in the quarter to give the Wildcats a 31-7 halftime lead.
Facing the nation's second-ranked defense, Washington struggled behind quarterback Ronnie Fouch, a redshirt freshman making his first college start. Fouch completed 12 of 28 passes for 181 yards and one touchdown, a 20-yarder to Michael Gottlieb midway through the fourth quarter. Fouch also threw an interception.
Going for their first bowl berth since 1998, the Wildcats are stacking wins against a schedule ranked 90th in the nation, according to NCAA statistics. Arizona's four victories have come against Idaho, Toledo, UCLA and Washington, which entered Saturday with a combined 2-16 record against major-college opponents.
After a visit to 3-3 Stanford next week, Arizona returns to Tucson to face Pac-10 contenders California on Oct. 18 and Southern California on Oct. 25.