Paxton threw a career-high 118 pitches and came an out away from tying his career high with seven innings pitched. The rookie lowered his ERA to 1.71, the best mark for a pitcher in his first 11 major league starts since 1990.
Cano's towering two-out home run in the first opened the scoring and was 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.
Texas starter Nick Martinez struggled through five innings, allowing five runs on six hits and four walks.
The Rangers put runners on the corners with two outs in the third after a review reversed a call at first base 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.
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.
Mariners: OF Chris Denorfia was scratched with a stiff neck a couple hours before to Tuesday's game. Chavez replaced Denorfia in right field.
Rangers: 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.
Mariners: Seattle planned 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.