Tyler Flowers and Alexei Ramirez singled with two away in the bottom of the inning against Adam Warren (1-2) and De Aza followed by hitting a 1-0 pitch to deep center.
New York let a four-run lead get away and Rivera eventually suffered his third blown save in 38 chances this season.
Chicago swept the three-game series, which were the first three games played this season by New York third baseman Alex Rodriguez.
Rodriguez officially appealed his 211-game suspension Wednesday, a ban brought about by Major League Baseball for his alleged use of performance enhancing drugs.
He is allowed to play while the appeal is ongoing and in his three games to date has gone 3-for-11.
The win went to Dylan Axelrod (4-8) despite the fact he gave up the lead in the top of the 12th. Axelrod was the eighth White Sox pitcher.
2014: The Year in Music [PHOTOS]