Kevin Kouzmanoff belted a two-run home run for the Rangers to snap a tie in the bottom of the seventh as the Rangers took a 6-4 lead they carried into the ninth inning.
The Rangers' top four hitters combined to go 8-for-8 against White Sox starter Felipe Paulino.
Jurickson Profar, Brent Lillibridge, Prince Fielder and Adrian Beltre each had two hits apiece, including a pair of RBI singles in the first two frames for Beltre.
The White Sox climbed on top in their first at-bat when designated hitter Mike McDade knocked in Avisail Garcia with an RBI single.
But Felipe Paulino gave the lead right back, struggling from the get-go for the South Siders. Paulino couldn't make it out of the second inning, allowing four runs on eight hits in 1 2/3 frames.
Rangers left-hander Robbie Ross wasn't especially sharp, but he managed to limit the White Sox to a run on two hits in two innings. Tanner Scheppers followed with two scoreless frames, during which he hit two batters but allowed only one hit.
The White Sox threatened against Scheppers in the top of the third, putting men on first and third with no one out. But Scheppers fanned McDade and got Connor Gillaspie to bounce weakly to first.
White Sox catcher Tyler Flowers launched a two-run homer in the top of the sixth, and the White Sox tied the game at four an inning later on an RBI single from Trayce Thompson.
Up next:: Jose Quintana, one of the more consistent and underrated American League starters over the course of the 2013 season, makes his Cactus League debut Monday against the Royals with a 2:05 p.m. CT first pitch at Camelback Ranch. The game will be featured on a whitesox.com webcast and also will include work out of the bullpen from Mitchell Boggs and Donnie Veal.