The Rangers (60-60) reached .500 for the first time since July 15 with their fourth straight win and seventh in eight games. The defending AL West champs, out of the division race behind Houston, pulled within 1 1/2 games of the idle Los Angeles Angels for the AL's second wild card.
Mazara's 16th home run capped the Rangers' second four-run inning, which included two injury replacements on the mound for the White Sox in their fifth straight loss.
The White Sox pulled within a run on Jose Abreu's 23rd homer, a solo shot in the ninth. But Alex Claudio finished a two-inning save for the left-hander's sixth of the season.
Reynaldo Lopez (0-1) gave up six runs and five hits in 4 1/3 innings.
Austin Bibens-Dirkx (4-2) retired all five batters he faced to pick up the win.
