The veteran 11th seed won in straight sets 6-4, 6-4 to book a date with Spain's Marcel Granollers. Haas could potentially meet Roger Federer in the third round.
Anderson will be left disappointed, especially after breaking into the world's top 20 for the first time earlier this week.
Results on Tuesday from the ATP and WTA Western and Southern Open (x denotes seed):
Men's singles
First round
Vasek Pospisil (CAN) bt Gilles Simon (FRA x15) 6-3, 1-1 ret (hip)
John Isner (USA) bt Florian Mayer (GER) 6-3, 6-4
Feliciano Lopez (ESP) bt Kei Nishikori (JPN x10) 6-4, 7-6 (7/4)
Nikolay Davydenko (RUS) bt Benoit Paire (FRA) 7-6 (10/8), 6-3
Tommy Haas (GER x11) bt Kevin Anderson (RSA) 6-4, 6-4
Benjamin Becker (GER) bt Pablo Andujar (ESP) 6-1, 6-4
Jarkko Nieminen (FIN) bt Edouard Roger-Vasselin (FRA) 6-3, 6-4
Tommy Robredo (ESP) bt Thomaz Bellucci (BRA) 6-7 (6/8), 7-6 (9/7), 6-2
Stanislas Wawrinka (SUI x9) bt Andreas Seppi (ITA) 6-3, 6-4
Mikhail Youzhny (RUS) bt Ernests Gulbis (LAT) 7-5, 6-3
Milos Raonic (CAN x12) bt Jack Sock (USA) 3-6, 6-4, 6-3
Second round
Grigor Dimitrov (BUL) bt Bryan Baker (USA) 6-3, 6-2
David Ferrer (ESP x3) bt Ryan Harrison (USA) 7-6 (7/5), 3-6, 6-4
Julien Benneteau (FRA) bt Radek Stepanek (CZE) 6-2, 5-7, 7-6 (7/4)
Roger Federer (SUI x5) def Philipp Kohlschreiber (GER) 6-3, 7-6 (9/7)
Women's singles
First round
Mona Barthel (GER) bt Lucie Safarova (CZE) 6-3, 6-4
Varvara Lepchenko (USA) bt Flavia Pennetta (ITA) 6-2, 2-6, 6-2
Jamie Hampton (USA) bt Anastasia Pavlyuchenkova (RUS) 7-5, 4-6, 6-3
Andrea Petkovic (GER) bt Daniela Hantuchova (SVK) 2-6, 6-4, 6-1
Elena Vesnina (RUS) bt Kirsten Flipkens (BEL x13) 3-6, 6-1, 6-3
Polona Hercog (SLO) bt Dominika Cibulkova (SVK) 6-2, 6-4
Magdalena Rybarikova (SVK) bt Julia Goerges (GER) 6-2, 4-6, 6-4
Ekaterina Makarova (RUS) bt Annika Beck (GER) 6-3, 6-2
Caroline Wozniacki (DEN x10) bt Peng Shuai (CHN) 6-1, 6-1
Alize Cornet (FRA) bt Ana Ivanovic (SRB x15) 2-6, 7-6 (10/8), 6-4
Monica Niculescu (ROM) bt Yanina Wickmayer (BEL) 6-1, 6-2
Jelena Jankovic (SRB x14) bt Sabine Lisicki (GER) 7-6 (7/5), 5-7, 6-2
Second round
Sloane Stephens (USA) bt Maria Sharapova (RUS x3) 2-6, 7-6 (7/5), 6-3