Paxton tossed a career-high 118 pitches and came an out away from tying his career high with seven innings pitched. His ERA is the best mark for a pitcher in his first 11 Major League starts since 1990.
"He was good," Rangers manager Ron Washington said. "I think he's one of their promising young arms. He throws the ball hard and has a good breaking ball."
Texas starter Nick Martinez struggled to keep the Rangers close in his five innings of work, allowing five runs on six hits and four walks.
Robinson Cano gave the Mariners an early lead with a towering two-out home run in the first, his 71st RBI of the year.
Seattle broke open a two-run game in the fifth, with the big blow coming on a double by Endy Chavez, which drove in a pair. Dustin Ackley scored Austin Jackson later in the inning with a single to stretch the lead to 5-0.
The Rangers put runners on the corners with two outs in the third after a review reversed a call at first and negated an inning-ending double play. Alex Rios grounded out, though, to end the threat. Texas failed to advance a runner past first base until Mike Carp took second on indifference in the ninth.
"They shut us down," Washington said. "We had a couple of chances to score runs and we just didn't."
Danny Farquhar did not allow a hit in the final 2 2-3 innings for the Mariners.
The Mariners avoided back-to-back losses for the first time since losing four straight from July 22-25.
TRAINER'S ROOM
Mariners: OF Chris Denorfia was scratched with a stiff neck a couple hours prior to Tuesday's game. Endy Chavez replaced Denorfia in right field.
Rangers: Rangers OF Alex Rios will have his right thumb reevaluated on Wednesday. Rios has been dealing with a bruised thumb for a week and it was heavily wrapped after Tuesday's game, but Washington said it was not the reason he pinch-hit for the veteran in the eighth. ... Texas still hasn't announced RHP Yu Darvish's season is over (elbow inflammation), but the likelihood that the Rangers' ace pitches again during the 2014 season is diminishing given that it would take time to work back into game shape.
UP NEXT
Mariners: Seattle plans to recall RHP Erasmo Ramirez from Triple-A Tacoma on Wednesday to start the matinee finale against Texas. Ramirez is 1-5 with a 4.04 ERA at the big league level this year, but hasn't allowed more than two runs his last six outings.
Rangers: RHP Colby Lewis looks to avoid the first four-game losing streak of his career and propel Texas to a series win.
CANO FINDING THE SEATS
Mariners 2B Robinson Cano has five home runs in August, the most he's had in any month this season.
ANDRUS STOPPED
Texas SS Elvis Andrus failed to reach base via a hit or walk, snapping a streak of 20 games against Seattle. Andrus had hits in 17 of the 20 games.