The Mariners took two of three from AL West-leading Texas. They scored three runs in 7 1-3 innings against Rangers ace Yu Darvish in the series finale.
Texas closer Joe Nathan (3-2) took over to begin the ninth with the score 3-all and Endy Chavez led off with a single. Humberto Quintero sacrificed and Nick Franklin drew a two-out walk before Seager's go-ahead hit.
Yoervis Medina (4-3) got the win and Danny Farquhar earned his seventh save in 10 tries.
The Mariners won for only the eighth time in 21 games. Each team scored single runs in the fifth, sixth and eighth innings before Seattle won it.
Darvish was coming off a start in which he struck out a career-high 15 and took a no-hit bid into the eighth against Houston.
The two-time All-Star from Japan struck out seven, raising his major league-leading total to 214, and gave up seven hits.
Darvish, who had 50 strikeouts in his last five starts, left after throwing 120 pitches. He walked four after walking a total of four in his previous three August starts.
Seattle took a 3-2 lead in the eighth when Seager walked on four pitches and Kendrys Morales singled off Darvish, and Dustin Ackley hit an RBI single off Robbie Ross.
Elvis Andrus hit a tying single in the Texas eighth.
NOTES: Michael Saunders got hits in each of his first three at-bats, all against Darvish. Saunders was 1 for 10 lifetime against Darvish going into the game.