De Aza was brushed back by Phil Coke with the bases loaded and then knocked a 1-2 fastball into right field to bring Avisail Garcia in from third with the decisive run.
Jeremy Bonderman (2-4) was hung with the loss after loading the bases and being pulled in favor of Coke.
De Aza and Garcia both had two hits in the win as did Alexei Ramirez. Garcia drove in two runs.
Addison Reed (5-1) pitched the final two innings for Chicago and picked up the win.