Seager has five home runs in four games, a power surge that started with a two-homer game against the Astros on Wednesday. He's also had at least two hits in all four games, tying a career-best streak.
Seager led off the seventh inning with his first home run and then gave Seattle the lead with his two-out bomb down the right field line in the eighth off Alexi Ogando (1-2). The comeback victory also gave the Mariners their first home series win against Texas since September 2012.
Danny Farquhar (1-0) pitched the eighth to earn the win and Fernando Rodney closed out the ninth for his fifth save.
Rangers starter Matt Harrison made his first appearance in more than a year, giving up two runs on three hits in six innings.
Harrison was activated from the disabled list before the game to make his first appearance since April 6, 2013. Harrison was the Rangers' opening day starter last season but only pitched two games before going on the disabled list with an inflamed nerve in his lower back. He had two back surgeries in a nine-day span a year ago, and another surgery on his right side in September. He battled stiffness in his back and neck during spring training, starting the season on the disabled list.
Harrison had no problems in the first three innings, retiring the first nine batters he faced. But a lengthy top of the fourth the Rangers had eight batters and scored three runs seemed to affect Harrison as he came out for the bottom of the inning.
Harrison walked Michael Saunders to lead off the fourth, and Robinson Cano got the Mariners' first hit with a one-out, run-scoring double. Harrison gave up another single and a walk to load the bases with two outs before striking out Seager to end the Seattle threat.
The Rangers took a 2-0 in the second inning. With runners on first and third and no outs, Mitch Moreland singled to right field. The ball got past Stefen Romero and the error allowed Alex Rios to score from first.
Texas added three more in the fourth inning. Leonys Martin drove in two runs with a single up the middle and Michael Choice had an RBI double that knocked Mariners starter Brandon Maurer from the game.
Cano singled in the sixth and later scored on a wild pitch from Harrison to cut the Rangers' lead to 5-2.
The Mariners now travel to New York for a three-game series against the Yankees starting on Tuesday. It's a homecoming for Cano, who spent the first nine years of his career with the Yankees.