Trailing 13-3 late in the third quarter, the Huskies (3-1, 1-0 Pac-12) scored on a 61-yard touchdown sprint from running back Bishop Sankey for their first offensive touchdown against an FBS opponent since the first quarter of the opener against San Diego State.
Then Washington put together a nine-play drive that included another fourth-down conversion and was capped by Williams' catch-and-run that gave the Huskies their first lead.
It was Washington's first win over a top-10 opponent since its upset of then-No. 3 USC in 2009, Steve Sarkisian's first season at Washington. And it was thanks to an inspired defensive effort that was the opposite of a year ago when Stanford (3-1, 1-1) bulldozed the Huskies to the tune of 446 yards rushing and 65 points.
Washington's student section poured on to the turf of CenturyLink Field after Price took a knee for the final time. It was a crucial win for the Huskies in the first game of a schedule that only gets tougher next week at No. 2 Oregon before returning home to host No. 13 USC.
Price finished 19 of 37 for 177 yards and the touchdown toss to Williams. Sankey had 144 yards on 20 carries after Stanford's defense had allowed just 124 yards rushing combined in the first three games of the season.
Washington started its winning drive at the 35 with 8:57 left and converted on fourth-and-1 at its own 44 with Dezden Petty bulling for 2 yards.
They eventually got down to the Stanford 35 with five minutes remaining.
That's when Sarkisian called for the quick screen to his star receiver.
Williams broke the tackle of Terrence Brown at the line of scrimmage then sprinted down the sideline ahead of safety Ed Reynolds, who caught up enough to knock the ball loose but only after Williams had crossed the goal line. Stanford, whose only touchdown came on Trent Murphy's 40-yard interception return in the third quarter, tried to put together one last drive.
Josh Nunes, who struggled in the first road start of his career, twice found Zach Ertz to get into Washington territory.
After converting on third-and-1 at the Washington 40, Nunes threw for Ty Montgomery down the sideline, but he dropped the pass at the Washington 5 with a clear path to the end zone.
Montgomery came back to catch a 6-yard pass on third-and-10, but that left the Cardinal facing fourth-and-4 at the 34 with two minutes left. With the defense spread out, Nunes tried to throw a fade route down the sideline to 6-foot-8 tight end Levine Toilolo. But the ball was poorly thrown and Desmond Trufant was in position to intercept the pass at the 8 with 1:46 left.
Stanford used its final two timeouts to force third-and-4, but Ben Gardner jumped offside giving the Huskies a first down and the chance to run out the clock.
Nunes, the replacement for Andrew Luck, finished 18 of 37 for 170 yards. But the most important factor was Washington's ability to control Stanford running back Stepfan Taylor.
Last year, Taylor ran for 138 yards against Washington and had 153 yards rushing in the upset of then-No. 2 USC on Sept. 15. He finished with 75 yards on 21 carries, none of them longer than 7 yards.
It was a victory for new Washington defensive coordinator Justin Wilcox. Given extra time to prepare for the Cardinal with a bye last weekend, he used every minute of it to devise a defensive scheme to slow Stanford's rushing attack.
Most notably, Wilcox regularly had eight or nine defenders near the line of scrimmage, daring Nunes to beat them through the air.
Stanford went more than 21 minutes of the first half without gaining a first down and Nunes couldn't lead a winning drive in the closing seconds. Stanford finished with just 235 yards of total offense, the fewest yards allowed by Washington since the 2010 Holiday Bowl against Nebraska.
Huskies Upset Stanford!
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