The Mariners, who entered the day tied with Kansas City and Tampa Bay for the second AL wild card, finished 6-3 on their road trip.
Cruz hit a two-run homer in the third, his 25th, then added his 26th in the fifth. It's the second multi-homer game in four days for the Mariners slugger, who has 22 RBIs in 13 games against the A's this season.
Seager homered in the first inning after Jean Segura and Cano singled.
All three home runs came off Oakland starter Jharel Cotton (5-9).
Emilion Pagan (1-2) pitched one-hit ball over 2 2/3 innings in relief of starter Yovani Gallardo to earn his first career win.
Edwin Diaz retired three batters for his 25th save.
Gallardo was knocked out of the game in the fifth inning after allowing three runs and six hits.
The Mariners, who went into the day with 67 errors, made two defensive gems.
Gamel made a leaping catch while crashing into the left-field wall to rob Marcus Semien of a hit in the fourth inning, the latest in a string a stellar plays from the rookie outfielder. Center fielder Jarrod Dyson also made a leaping catch near the wall in center in the first inning.
Cotton, winless since June 23, allowed six runs and eight hits over six innings.
Athletics: RHP Bobb Wahl will see a shoulder specialist in Dallas on Friday. Wahl has been on the disabled list since May 24 with a strained pitching shoulder. He had been attempting a comeback on a rehab assignment but was shut down after experiencing soreness.
Mariners: LHP James Paxton (12-3, 2.70 ERA) pitches in the opener of a four-game series against the Angels on Friday night in Seattle. Paxton leads the AL and is tied for second in the majors with 113 wild pitches.
Athletics: RHP Chris Smith (0-1, 4.82) faces Baltimore on Thursday night. The 36-year-old is seeking his first career win as a starter.