Keith Price passed for 342 yards and two touchdowns on 28-of-35 passing, while Jesse Callier carried the ball six times for 66 yards and a score for the Huskies (2-0), who posted an impressive 38-6 victory over Boise State in their season-opener prior to last week's bye.
Nathan Scheelhaase completed just 9-of-25 passes for 156 yards, one touchdown, and one interception while adding 21 yards and a score on 12 carries for the Fighting Illini (2-1), who were coming off a 45-17 victory over Cincinnati.
"You saw last week with Cincinnati that we were able to put the pressure on them early, but today we felt like we left points out there in the first half," Scheelhaase said.
After Illinois kicker Taylor Zalewski missed a 41-yard field goal early in the second stanza, Price put his squad on the board less than three minutes later.
The Washington signal-caller completed all five of his passes on an 8-play, 77-yard series that he capped with a short dump off to Sankey, who scampered 31 yards down the right sideline to make it 7-0 just under four minutes into the second.
Zalewski connected on a 40-yard field goal on Illinois' ensuing touch to get the Illini on the board, but Travis Coons nailed a 23-yarder in the waning seconds of the half to send the Huskies into the break with a 10-3 edge.
Washington extended its lead on the opening touch of the second half, as Sankey carried the load on a 7-play, 75-yard trek that the running back capped with a 1-yard TD surge to make it 17-3 less than two minutes into the third.
Scheelhaase countered with a scoring march of his own, converting a 3rd-and-7 from the Washington 33 with an 11-yard pass to Martize Barr.
After three straight runs moved the Illini to the Washington 2, Scheelhaase bootlegged to his right and surged into the end zone for a 2-yard score to bring Illinois within 17-10 with 9:14 left in the third.
On Washington's ensuing touch, Price picked up a first down with a 14-yard strike to Kevin Smith on 3rd-and-4 before Callier broke free for a 39-yard score to push Washington's lead to 24-10 midway through the third.
After a quick three-and-out from the Illini, Price completed all three of his passes on a 5-play, 78-yard scoring strike, culminating in a 9-yard TD toss to Jaydon Mickens to make it 31-10.
Illinois answered on its next play from scrimmage, as Scheelhaase found Ryan Lankford streaking down the middle of the field for a 72-yard touchdown to trim the Illini's deficit to 31-17 with 3:16 left in the third.
Illinois cut into the margin early in the fourth, as wide receiver Miles Osei received a toss on a reverse before firing down the field for Matt LaCosse, who hauled in the 35-yard reception at the Washington 19.
Facing 4th-and-1 from the Washington 10 later in the drive, freshman quarterback Aaron Bailey kept it himself and went untouched into the end zone off the left side for a 10-yard score to bring Illinois within 31-24 with 9:10 remaining.
Washington chewed up over 4 1/2 minutes of clock on its ensuing possession, but the drive stalled inside the Illinois 20 and the Huskies settled for a 32- yard field goal from Coons to push the margin to 34-24 with 4:44 left.
After converting a 3rd-and-6 with an 11-yard scamper on Illinois' next touch, Scheelhaase was hit as he threw and the ball ended up in the arms of Washington's Gregory Duce to give the Huskies possession with 3:51 remaining.
Washington then went to its workhorse, feeding Sankey on five straight plays to run out the remainder of the clock.
"I think we did a good job, digging deep down the stretch and we finished," Sankey said. "We knew we just had to take it upon ourselves and fix the things that we needed to fix and just finish."
Washington holds a 6-4 lead in the all-time series against Illinois ... The Huskies outgained Illinois, 615-327 ... Smith finished with five catches for 104 yards for the Huskies ... Lankford hauled in three passes for 100 yards for Illinois.
09/14 23:20:14 ET