Michael Saunders walked on a full-count pitch with two out before Seager connected against Robbie Ross (4-2) for his third hit of the game. Seager's 12th homer landed in the first row of seats in right field.
Charlie Furbush (2-4) pitched 1 2/3 scoreless innings for the win, and Tom Wilhelmsen was perfect in the 10th for his 17th save.
The Mariners last won two straight in Texas on May 29-30, 2012, when they took the last two of a three-game series. They'll go for a sweep Thursday night.
The Rangers dropped to 30-14 at home against Seattle since the start of 2009.
David Murphy and Ian Kinsler homered in the fifth inning against Felix Hernandez, giving Texas a 2-1 lead. The leadoff shot by Murphy ended a four-game streak without a homer for the Rangers, their longest in more than two years.
It also was the first homer for Murphy since June 9, and his first RBI since June 11.
Kinsler, who spent nearly a month on the disabled list with a rib fracture, sent the 11th pitch of the at-bat from Hernandez a few rows deep in left field for his first homer since May 8.
The Mariners pulled even with a run in the sixth, ending Derek Holland's night with a 37-pitch inning that included three straight full counts.
The last of the three full counts came against Mike Zunino, who battled back from an 0-2 count for a tying infield single on a hopper that Adrian Beltre couldn't handle behind the bag at third.
Raul Ibanez and Kendrys Morales opened the inning with singles, and Justin Smoak walked with one out. Dustin Ackley struck out on a full count before Zunino's hit brought home Ibanez.
Texas center fielder Leonys Martin went 0-for-4 to end the longest active hitting streak in the majors at 15 games.
Holland, making his first outing since a two-hit shutout in a 2-0 win at Yankee Stadium, gave up a leadoff home run to Jason Bay on the fourth pitch of the game.
The Mariners had runners at first and third with no outs in the second after singles by Seager and Smoak, but Holland got a shallow fly ball from Dustin Ackley that forced Seager to hold up after going a third of the way down the line. Holland then struck out Zunino and got Brad Miller on a fly ball to center.
Holland struck out 10 and had seven hits and two walks on his line.
Hernandez gave up four extra-base hits, matching the Texas total from its previous four games combined. Besides the homers from Murphy and Kinsler, Nelson Cruz doubled with two outs in the first and Adrian Beltre had a leadoff double that was followed by three straight outs in the sixth.
Elvis Andrus grounded into an inning-ending double play with two on in the seventh to wrap up the night for Hernandez, who gave up seven hits and struck out seven in his third straight no-decision.
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