Chris Polk converted a key fourth-down run, and Jake Locker tossed a 27-yard touchdown pass to Jermaine Kearse in the right corner to give the UW the lead back with 44 seconds to go.
Jeff Tuel had WSU back even with the favored Huskies.
Tuel accounted for his second touchdown of the fourth quarter, this time a 16-yard pass to Marquess Wilson, and the game is tied at 28 with 4:26 remaining.
On the 73-yard march, Tuel connected twice with Daniel Blackledge - on completions of 32 and 26 yards.
Every time the UW scores, the Cougars answer.
After a long Polk scoring run put the Huskies up 28-14, WSU's Tuel led a 10-play, 74-yard drive to keep the the Cougars alive in the 103rd Apple Cup.
Tuel capped it with a 1-yard touchdown sneak at the 8:46 mark.
One play after the Huskies stopped WSU on fourth-and-1, running back Polk dashed 57 yards for a touchdown to extend the lead to 28-14.
Polk now has a career-high 220 rushing yards. The last UW rusher to eclipse 200 yards was Louis Rankin against California in 2007.
Rashaan Shehee had 212 rushing yards in the 1995 Apple Cup - the last 200-yard game in the rivalry game.