Paxton (8-3) scattered five hits and allowed two earned runs on a night when the left-hander and the Mariners' bullpen combined to strike out 15 White Sox hitters.
Edwin Diaz picked up his 14th save with a scoreless ninth inning.
Cano's third-inning blast gave his team's pitchers all the offense they needed as the Mariners opened the season's second half with their fifth victory in the last 15 games.
Matt Davidson and Tyler Saladino hit RBI doubles for the White Sox, who didn't manage a hit after the fifth.
Chicago starter James Shields allowed four runs and seven hits in six innings.
The Mariners jumped out to a 3-1 lead in the third inning after Cano blasted his 18th home run of the season off the top of the right field wall. Cano belted the first pitch he saw from Shields after Mike Zunino walked and Jean Segura singled earlier in the inning.
The White Sox got to within 3-2 in the fourth inning on a Davidson double that scored Avisail Garcia, who singled and then stole second. But the Mariners quickly extended their lead back to two runs in the fifth when Segura, who doubled to lead off the inning and advanced to third on a Cano groundout, scored on a wild pitch by Shields.
Saladino gave the White Sox a 1-0 lead in the second inning with an RBI double that scored Garcia, who singled with one out. Garcia advanced to third with a stolen base and a Zunino throwing error. After Davidson struck out, Saladino, who was activated off the disabled list on Friday, lined a ground-rule double into the right field corner.
NOTES: The Mariners promoted Nasusel Cabrera to interim bullpen coach to replace Mike Hampton, who resigned July 2 to spend more time with his family. Cabrera has worked as a batting practice pitcher and assistant coach since joining the Mariners' major league staff in 2015. ... The White Sox activated RHP Miguel Gonzalez off the 10-day disabled list after he had been sidelined since June 15 with A/C joint inflammation in his right shoulder. Gonzalez is 4-8 with a 5.49 ERA in 13 starts this season. ... Chicago IF Tyler Saladino was activated from the 10-day disabled list after he had been out since May 27 with back spasms. Saladino is hitting .204 with five RBIs and 10 runs in 31 games. Saladino batted seventh and started at second base.