Hisashi Iwakuma (11-6) struck out eight and allowed one run in seven innings.
Derek Holland pitched two-hit ball with six strikeouts over seven scoreless innings for Texas before Neal Cotts (4-2), whose 0.93 ERA was the lowest among American League relievers, walked Franklin. Seager then lined a shot into the Rangers bullpen in right-center field, his 18th homer of the season but first in 13 games.
Justin Smoak homered in the ninth for Seattle, which won for only the seventh time in 19 games.
The Rangers had the bases loaded in the eighth when A.J. Pierzynski, whose RBI single in the fourth produced the only Texas run, had an inning-ending popout to third base.
After Mariners reliever Oliver Perez walked and hit a batter to start the eighth, the only batters he faced, Elvis Andrus had a sacrifice bunt before Ian Kinsler struck out. Adrian Beltre, already with two hits and hitting .452 over a 16-game span, was intentionally walked before Charlie Furbush came on to retire Pierzynski.
Danny Farquhar struck out two in a perfect ninth for his sixth save in nine chances.
Rangers manager Ron Washington twice went out to argue calls by Angel Hernandez, an umpire he publicly criticized in the past. Both calls were for players coming off second base - one defensively, the other a Texas base runner.
In the Seattle third, Rangers second baseman Kinsler was taking a throw for a force out when he shuffled his feet while trying to get out of the way of an oncoming runner. Hernandez immediately motioned that Kinsler came off the base before making the catch, and replays showed that to be the case.
An inning later, on his RBI single to left-center, Pierzynski was called out at second after sliding in ahead of the tag by Nick Franklin before briefly coming off the base. It didn't appear on replays that Pierzynski was being tagged when he came off before reaching out with his hand to get back on the base. Hernandez, behind the tangled bodies, called the runner out, bringing Washington out again as Pierzynski was flat on back screaming in disgust.
Two years ago, after Washington and first base coach Gary Pettis got ejected by Hernandez on a disputed balk call, the Rangers manager said, "Angel is bad. That's all there is to it."
Even before his reunions with Hernandez, Washington had gone out to talk with umpire Doug Eddings about an inning-ending play in the first when Andrus tried to score from first on Beltre's single to right. Andrus dived head-first, but was initially blocked from reaching the plate while catcher Humberto Quintero made a sweeping tag. It was unclear on replays if he actually tagged Andrus, or if the runner ever did touch the plate.
NOTES: Seager has a 12-game hitting streak at Rangers Ballpark. ... When Andrus tried to reach on a bunt leading off the sixth, Quintero bounced up to field the ball and then made a strong throw even while one of his cleats came off his feet. ... Rangers ace Yu Darvish (12-5), the major league strikeout leader with 207, turned 27 on Friday. He starts the series finale against the Mariners on Sunday. ... When Jurickson Profar struck out to end the second, he contended that the ball bounced in the dirt after he fouled it off. Eddings got the ball back from Quintero, who was already going back to the dugout, and confirmed the strikeout. He showed the ball to Profar. Replays, though, showed it might have bounced into the catcher's mitt.