Chicago's Philip Humber took the mound for the first time since he threw the 21st perfect game in baseball history last weekend and he struggled from the start.
Humber (1-1) gave up four hits and two runs in the first inning alone and he eventually labored through five frames, surrendering nine runs on eight hits with three walks.
Youkilis hit his grand slam in the third to give Boston a 6-1 lead and Saltalamacchia added a solo shot later in that inning.
Saltalamacchia tacked on a two-run blast in the fifth, his fourth homer of the season.
Boston won its fourth in a row and handed the White Sox their third straight setback.
The win went to Felix Doubront (1-0), who gave up three runs on five hits in six innings. It was Doubront's first major league victory in two years and only the third of his career.