"This is just one game," he said. "We've got a lot more games to go."
In the first half, the teams combined to score touchdowns on seven consecutive possessions.
The streak started when Luke Falk threw a 53-yard touchdown pass to Marks and the Cougars led 7-0 midway through the first quarter.
Eastern Washington replied with Gubrud's 14-yard touchdown pass to Antoine Custer Jr., to tie the game at 7-7.
Washington State came right back with a 58-yard drive, capped by Falk's 27-yard scoring pass to Kyle Sweet for a 14-7 lead.
Eastern Washington replied with another touchdown, this time on a 6-yard pass from Gubrud to Sam McPherson. On this 75-yard drive, Kupp caught one pass for 11 yards, rushed the ball once for 14 yards and threw a 22-yard pass.
Washington State came right back, scoring on a 2-yard pass from Falk to Marks.
Eastern Washington tied the game at 21-21 when, on the first play of its subsequent possession, Kupp caught a 75-yard touchdown pass from Gubrud.
Jamal Morrow's 5-yard touchdown run put the Cougars ahead 28-21, and ended the scoring streak as EWU punted on its next possession.
But Eastern Washington's Mitch Fettig intercepted a Falk pass, and Jordan Dascalo kicked a 48-yard field goal as time expired to cut Washington State's lead to 28-24 at halftime.
Kupp caught a 26-yard touchdown pass from Gubrud on the opening drive of the second half to put the Eagles ahead 31-28. That gave him 58 career touchdown passes, tying the FCS record set by David Ball of New Hampshire. He broke the record on EWU's next drive, with a one-handed catch of Gubrud's 7-yard pass in the end zone, giving the Eagles a 38-28 lead.
Marcellus Pippins intercepted Gubrud in the end zone to end another EWU scoring threat.
Erik Powell missed a 38-yard field goal attempt for Washington State midway through the fourth.
Gerard Wicks caught a 9-yard touchdown pass from Falk with 4:42 left in the game for Washington State's first points of the second half, cutting EWU's lead to 38-35.
But Eastern Washington marched down the field, with Gubrud scoring on a 30-yard bootleg with 1:39 left for a 45-35 lead.
Wicks scored on a 3-yard touchdown run for Washington State with 14 seconds left. Their on-side kick attempt was recovered by the Eagles.
Coach Mike Leach has lost all five of his season openers at Washington State.
Eastern Washington: Gubrud, a sophomore, played spectacularly in his first career start. Kupp has made a specialty of out-classing Pac-12 defensive backs. Last season, he caught 15 passes for 246 yards at Oregon. Two years ago he caught three touchdown passes against Washington. As a freshman, he caught five passes for 119 yards and two touchdowns against Oregon State.
Washington State: The Cougars finished 9-4 last year, but will have to play better in a tough Pac-12 to match that this year.
Eastern Washington plays at FCS powerhouse North Dakota State next Saturday
Washington State plays at Boise State on the blue turf next Saturday.
COOL HAND LUKE
Falk completed 41 of 51 passes for 418 yards and four touchdowns. He was intercepted once.
Washington State received plenty of votes in the preseason Top 25, but likely won't get many in the next poll.