Fister (5-11) scattered five hits over five innings and pitched out of several jams while leading the Mariners to their first win at the Coliseum since Opening Day. Seattle had lost six straight in Oakland since then.
Kurt Suzuki singled twice and drove in two runs for the A's, who missed a chance to gain ground on first-place Texas in the AL West.
Eight of Seattle's nine starters had at least one hit and six players scored. Before Tuesday, the Mariners had not scored more than three runs in 11 consecutive games, the second-longest stretch in franchise history.
They did it against Oakland starter Dallas Braden, who pitched a perfect game against Tampa Bay in May and had won five of his previous eight starts.
Seattle jumped on Braden early, scoring five runs in the second inning after the left-hander had retired the side in order in the first. The Mariners punched out seven hits in the second, all singles, and scored five runs.
Moore homered off Braden in the third to make it 6-0.
Braden (9-11) had allowed only one earned run over his previous 14 innings. He left after five innings, giving up nine hits.
Fister, winless in his previous four starts, didn't make it easy on himself. The right-hander loaded the bases in the first and had runners on second and third with one out in the second but escaped both times.
He wasn't as fortunate in the fifth but kept the damage to a minimum.
Cliff Pennington walked and Rajai Davis singled. After Daric Barton fouled out, Suzuki lined a two-run single to center to trim the gap to 6-2. Fister then walked Jack Cust but got the last two batters on fly outs to end the threat and his night.
Fister's win is his first since Aug. 8 and only the second in his last 17 starts. The 26-year-old missed nearly three weeks in June with fatigue in his right shoulder and made one rehab outing in the minors before returning to the big league club.
The A's loaded the bases against reliever Garrett Olson in the sixth and came away empty again when Olson got Suzuki to ground out.
Seattle's bullpen nearly melted down and gave the big lead away.
Oakland pinch-hitter Coco Crisp, not in the lineup due to a sore left knee, hit a two-run single in the ninth off Brandon League to drive in Cust and Ellis. Crisp later scored on a wild pitch to make it 7-5 before David Aardsma got Pennington to fly out and end the game for his 29th save in 34 tries.
Oakland had a chance to improve its fading playoff hopes after Texas lost to Toronto earlier in the day. Instead, the A's remain seven games behind the Rangers with 24 to go.
Ichiro Suzuki had two hits for Seattle, giving him 2,211 for his career and moving him into a tie for 169th place with Willie McCovey on the all-time list.
Notes: Oakland OF Jeremy Hermida went 1 for 4 after being selected from Triple-A Sacramento earlier Tuesday. Hermida, who began the season with Boston before being released by the Red Sox on Aug. 31, takes the roster spot left vacant when Oakland optioned RHP Vin Mazzaro to Sacramento on Monday. ... Phil Hellmuth, winner of 11 World Series of Poker bracelets, threw out the first pitch. ... Seattle interim manager Daren Brown plans to give each of his five starting pitchers an extra day's rest the next two times through the rotation. ... A's rookie Steve Tolleson had a career-high three hits.