De Aza's two-bagger with two out in the second inning sent home Dayan Viciedo and Hector Gimenez, breaking a 2-2 tie and putting the White Sox ahead to stay.
Adam Dunn smacked a two-run homer for Chicago, which notched a fifth victory in six games overall.
Dylan Axelrod (3-3) recovered from a rocky start to earn the victory, allowing three runs on six hits over 5 1/3 innings.
Marlins starter Alex Sanabia (3-7) was touched for four runs on six hits over four frames.
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