Scott Proctor (1-3) picked up his first win with a scoreless inning of relief.
Mariano Rivera entered the game in the eighth inning with the Yankees owning only a one-run lead and worked 1 2/3 innings for his seventh save.
New York won three out of four from the White Sox.
The loss went to Jose Contreras (4-6), who gave up four hits and three runs over 7 1/3 innings.
Chicago tied it in the seventh, but Abreu keyed a three-run eighth with his double. The grand slam by Rodriguez was part of a six-run ninth.
Celebrity Families of 2014 [PHOTOS]