The SA men's number one twice fought back from a set down to beat Spaniard Fernando Verdasco, the former world number seven, 4-6, 6-3, 4-6, 7-6, 6-2 in the third round of the men's singles competition.
Anderson had previously reached the third round of the US Open in 2010 and 2011 and last year's French Open.
VIDEO: Post-match interview with Kevin Anderson
He faces world number six Tomas Berdych of the Czech Republic in the fourth round in Melbourne.
Berdych beat Austrian Jurgen Melzer in straight sets on Friday to set up the match against Anderson.
Results from day five of the Australian Open on Friday:
Women's singles
Third round
Julia Goerges (GER x18) bt Zheng Jie (CHN) 6-3, 1-6, 7-5
Angelique Kerber (GER x5) bt Madison Keys (USA) 6-2, 7-5
Agnieszka Radwanska (POL x4) bt Heather Watson (GBR) 6-3, 6-1
Li Na (CHN x6) bt Sorana Cirstea (ROM x27) 6-4, 6-1
Ana Ivanovic (SRB x13) bt Jelena Jankovic (SRB x22) 7-5, 6-3
Ekaterina Makarova (RUS x19) bt Marion Bartoli (FRA x11) 6-7 (4/7), 6-3, 6-4
Kirsten Flipkens (BEL) bt Valeria Savinykh (RUS) 6-2, 4-6, 6-3
Maria Sharapova (RUS x2) bt Venus Williams (USA x25) 6-1, 6-3
Men's singles
Third round
Novak Djokovic (SRB x1) bt Radek Stepanek (CZE x31) 6-4, 6-3, 7-5
Kevin Anderson (RSA) bt Fernando Verdasco (ESP x22) 4-6, 6-3, 4-6, 7-6 (7/4), 6-2
Janko Tipsarevic (SRB x8) bt Julien Benneteau (FRA x32) 3-6, 6-4, 2-6, 6-4, 6-3
Kei Nishikori (JPN x16) bt Evgeny Donskoy (RUS) 7-6 (7/3), 6-2, 6-3
Stanislas Wawrinka (SUI x15) bt Sam Querrey (USA x20) 7-6 (8/6), 7-5, 6-4
Nicolas Almagro (ESP x10) v Jerzy Janowicz (POL x24) 7-6 (7/3), 7-6 (7/4), 6-1