Anderson surprised the Serb 6-3, 7-5 to set up a second-round match with fellow young American wild card Donald Young, who prevailed 7-5, 6-0 over Israeli Dudi Sela.
Seventh-seeded Belgian Xavier Malisse was a straight-set winner over American qualifier Ryan Sweeting 7-6 (7-1), 6-3. Malisse moves on to face Illya Marchenko, who won Monday.
Also in Atlanta, an all-American battle between Taylor Dent and James Blake saw Dent prevail 6-3, 3-6, 6-4, while American Robby Ginepri moved on with a 7-6 (7-4), 6-2 decision over qualifier Nick Lindahl of Australia.
Celebrity Couples of 2014 [PHOTOS]