Andrew Vaughn knocked his 21st home run of the season over the wall in left center field to bring home Yoán Moncada, who walked to get on base, in the bottom of the second inning.
Diamondbacks would cut the lead in half in the top of the third on a Ketel Marte sacrifice fly after a Corbin Carroll triple.
Yoán Moncada would knock his own homer 400 feet game to return the Sox lead back to two.
Touki Toussaint took the mound to start the game, tossing 4.0 IP and fanning four. Tanner Banks, Declan Cronin and Aaron Bummer struck out one each and Bryan Shaw secured the win.