Washington State (1-1), which lost at BYU in the season opener, also unveiled a $65 million upgrade of Martin Stadium in front of the first sellout crowd here since 2007.
Eastern Washington (1-1), an FCS power coming off a victory over Idaho of the FBS, kept it close behind a pair of touchdown receptions by Brandon Kaufman.
This was the first meeting since 1908 between the two programs, located 60 miles apart.
Washington State scored first when Tuel connected with Myers in the back of the end zone on a 2-yard scoring pass with 5:42 left in the first quarter. It was their first touchdown of the season after being held to two field goals by BYU.
Eastern replied on the next series when quarterback Kyle Padron hit Kaufman with a 93-yard touchdown pass to tie the score. But Washington State drove 75 yards on its next series, with Carl Winston rushing over from the 1 to take a 14-7 lead. Winston's 27-yard run was the key play of the drive.
Washington State's Cyrus Coen intercepted a scrambling Padron and ran the ball down to Eastern's 17. On the first play, Tuel passed 17 yards to Myers for a touchdown that put WSU up 21-14.
A 60-yard field goal by WSU's Andrew Furney as time expired gave the Cougars a 24-14 halftime lead. It was the second longest field goal in team history after Jason Hanson's 62-yarder against UNLV in 1991.
The third quarter was scoreless.
Washington State had first-and-goal on the EWU 2 in the fourth quarter, but Teondray Caldwell fumbled on a run and EWU's Allen Brown recovered. The Eagles went on a penalty-filled 99-yard drive that ended with a 17-yard touchdown pass from Padron to Kaufman. The extra point was blocked to leave WSU with a 24-20 lead with 2:17 remaining.
Washington State recovered the onside kick, had two touchdown plays called back because of penalties, and had to punt. Eastern got a last chance with 1:29 left from its 17, but could not score.
Washington State has never lost in 17 games against teams from the FCS. Eastern Washington is 8-21 against FBS teams.