The Rangers (82-64) registered a sixth consecutive victory and moved one game ahead of the Mariners (81-65) in the race for the second American League wild card. The Blue Jays (80-67) fell 1 1/2 games behind Seattle.
Jonah Heim added a solo home run for the Rangers to finish with eight RBIs in the series.
Vladimir Guerrero Jr. hit a two-run home run for the Blue Jays, who are 3-4 on their 10-game homestand.
Toronto right-hander Kevin Gausman (11-9) allowed four runs, six hits and six walks with five strikeouts in 4 2/3 innings.
Texas right-hander Nathan Eovaldi gave up two runs, three hits and three walks with three strikeouts in 3 1/3 innings.
Cody Bradford (4-1) replaced Eovaldi and allowed a walk and a hit while fanning four in 2 2/3 innings.
Seager opened the scoring with his 31st homer of the season, a drive to right-center with one out in the first.
Bo Bichette singled with one out in the home first, and Guerrero hit a blast to the second level in the left for his 22nd homer of the season and a 2-1 Toronto lead.
Texas regained the advantage in the second on Ezequiel Duran's bunt single, Marcus Semien's walk and Seager's two-run double to left that popped out of the glove of Whit Merrifield as he went into the wall.
Heim hit a two-out blast to center with two outs in the third, his 17th homer of the season, for a 4-2 lead.
Duran started the eighth with a double against Toronto reliever Trevor Richards, and Evan Carter walked. Semien followed with an RBI double.
After an intentional walk to Seager, Nathaniel Lowe hit a two-run single. Pinch hitter Leody Taveras loaded the bases with a bunt single against Yimi Garcia, and Robbie Grossman walked, forcing in a run. One out later, Josh H. Smith hit a sacrifice fly to cap the scoring.
Rangers designated hitter Mitch Garver left after fouling a ball off his foot in the fourth inning.
Toronto reinstated third baseman Matt Chapman (sprained right middle finger) from the injured list and optioned outfielder Nathan Lukes to Triple-A Buffalo. Chapman went 0-for-3 with a walk in his first game since Aug. 27.
—Field Level Media