Rosales' two-run blast in the top of the second was the lone black mark on an otherwise dominant performance by Chicago ace Chris Sale (10-2), who struck out nine and yielded just three hits over six innings, despite receiving his second setback of the season.
The utility man added a solo shot off Daniel Webb in the seventh inning to help Texas record back-to-back victories for the first time since June 27-28.
Tepesch (4-7) halted a long drought of his own after scattering six hits and a walk. The right-hander had dropped four straight decisions since besting Minnesota to begin the Rangers' two-game streak in late June.
The White Sox, outscored by a 46-15 margin in losing four of five, got their lone run on a Dayan Viciedo solo homer in the seventh. Alexei Ramirez finished 3-for-4 in defeat.