Josh Reddick also hit a two-run home run while John Jaso went 3-for-5 with two runs scored for the Athletics, who have won six straight. Drew Pomeranz (3-1) gave up just three hits and two walks while striking out eight over five innings to win his second straight start.
Scott Carroll (1-3) dropped his third straight start as he was touched for six runs on 11 hits over five innings for the White Sox, who have dropped four straight.
An RBI double from Moss in the first inning got Oakland on the board and the team took a 2-0 lead in the fourth thanks to a run-scoring single from Craig Gentry.
The Athletics extended their lead with a four-run fifth inning. Jaso doubled to start it and scored on a Yoenis Cespedes double. Derek Norris' double plated Cespedes, and Reddick followed with his second home run of the season for a 6-0 lead.
In the seventh, the A's scored three more runs on an RBI double from Jed Lowrie and two-run home run by Moss for a 9-0 advantage.
Pomeranz didn't allow a runner past second in his work, while Dan Otero worked a pair of flawless innings in relief.
Fernando Abad gave up a leadoff single to Conor Gillaspie in the eighth, but got Leury Garcia to hit into a double-play and struck out Marcus Semien to end the inning.
Moss' second two-run home run of the game in the eighth made it an 11-0 game.
Joe Savery closed out the game with a quiet ninth.