Minor (3-2) matched the team record for strikeouts by a left-hander while allowing just three hits in his 111-pitch outing. He could have departed with the Rangers up big in the sixth, but he stayed in.
"I felt like the bullpen needed it," Minor said.
It was a timely performance after Rangers' bullpen picked up the loss in two of the previous three games.
"He understands the value of that extra inning," Texas manager Chris Woodward said. "Then obviously he goes out and strikes out two more guys to get his career high, which is cool."
Andrus and Odor each hit a three-run homer for Texas, which finished with a season-high 20 hits. Joey Gallo hit a solo drive for his ninth homer, and Logan Forsythe finished with four hits and three RBI.
Other than Domingo Santana's deep drive in the first inning, Minor went largely unchallenged by the usually heavy-hitting Mariners, who lead the league in extra-base hits.
"He's able to use all his pitches in any spot any time," Woodward said. "He's got a lot of weapons and he's showing them off right now."
Seattle hurt itself with three errors, and Mike Leake (2-3) was tagged for five earned runs and 10 hits in five innings.
Leake surrendered a one-out double to Forsythe in the second, and Jeff Mathis got on when Mallex Smith dropped a fairly routine running catch in center. After Choo popped out, Odor belted a drive to right for his first homer.
It was Texas' third road win of the season in 12 tries.
"I have no words of wisdom -- that was a rough ballgame," Servais said. "We did that to them a couple nights ago and they turned around and flipped it on us tonight. You know, we've got to play good defense, and certainly we made some costly errors that didn't help out Mike Leake at all tonight."
ON THE WAY
Mariners third baseman Kyle Seager said he is ahead of schedule in his return from surgery on his left hand and could take live batting practice soon. Seager is eligible to return May 25.
He threw on the side before Saturday's game and was happy to be back in the clubhouse with the team.
"Watching them on TV and watching them in Japan and everything was definitely weird for me," Seager said.
Mike Wright pitched two innings for Seattle in his first appearance since he was acquired in a trade with Baltimore. He allowed one run and three hits.
Rangers: An MRI on Taylor Hearn's left elbow showed inflammation but no acute injury, the team said. The left-hander was placed on the 10-day injured list after complaining of soreness following a disastrous call-up start Thursday that ended after one-third of an inning. ... INF Asdrubal Cabrera remained out with a calf strain, but he is expected to play Sunday.
Mariners: 2B Dee Gordon got what Servais characterized as a spa day after he limped off the field following his game-ending slide at second base Friday night that allowed the winning run to score in a 5-4 victory in 11 innings. He is expected to play Sunday.
Rangers: RHP Lance Lynn (2-2, 6.61 ERA) starts the finale of the four-game set on Sunday. Lynn was hit hard in his previous outing, allowing eight runs in 3 1/3 innings in an 11-5 loss at Oakland.
Mariners: RHP Erik Swanson (0-2, 4.61 ERA) makes his third career start.
Fantasy baseball: Top six pickups to add stolen bases
Stolen bases are hard to add at this point in the season, but Eric Karabell breaks down the best base thieves left, and how important steals are down the stretch.
Cole Hamels agrees to deal to return to MLB with Los Angeles Dodgers, sources say
Cole Hamels, who pitched in just one game for the Braves during the 2020 season because of shoulder and triceps issues, has agreed to a deal with the Dodgers that would provide insurance for Los Angeles' rotation, sources confirmed to ESPN.
Fantasy baseball forecaster: Team hitting ratings
Stay ahead of the game and optimize your fantasy baseball hitters with our forecaster, which provides a rolling 10-day outlook of every team's hitting matchups as well as the potential for stolen bases.
Fantasy baseball forecaster: Pitcher projections for the next 10 days
Keep up to date on who is pitching -- and how well they're expected to do -- with our forecaster, which provides a rolling 10-day outlook of every team's probable starting pitchers with game score projections.
Stock Watch: Where all 30 teams stand for 2021 and beyond after epic MLB trade deadline
How did the wildest, most thrilling flurry of deals we've seen in ages change the fortunes of your favorite team?
Inside one of the wildest trade deadlines in MLB history -- and where season goes from here
From what shaped Jed Hoyer's strategy to how the Dodgers got their blockbuster deal across the finish line, here's how the biggest moves played out behind the scenes and what they mean for the rest of 2021.