The South African No 1 will next face Marcos Baghdatis from Cyprus in the second round on Friday.
Baghdatis defeated Japan's Go Soeda 6-4, 6-3, 6-1 in his first round match.
Meanwhile, South Africa's top women's player, Channelle Scheepers, is in action on Thursday against former world No 1 Caroline Wozniacki.
Scheepers advanced to the next round after beating compatriot Chanel Simmonds 2-6, 6-2, 6-2 in the first round.
US Open results on Wednesday (x denotes seeded player):
Men's singles
First round
Alex Bogomolov (RUS) bt Benoit Paire (FRA x24) 7-5, 2-6, 6-4, 5-7, 7-6 (7/5)
Tim Smyczek (USA) bt James Duckworth (AUS) 3-6, 6-2, 6-4, 6-1
Marcel Granollers (ESP) bt Jurgen Zopp (EST) 6-1, 3-6, 1-6, 6-3, 6-4
Rajeev Ram (USA) bt Fabio Fognini (ITA x16) 6-1, 6-2, 6-2
Aleksandr Dolgopolov (UKR) bt David Goffin (BEL) 6-2, 6-4, 6-4
Mikhail Youzhny (RUS x21) bt Nicolas Mahut (FRA) 6-4, 6-4, 7-6 (7/4)
Evgeny Donskoy (RUS) bt Jurgen Melzer (AUT x29) 7-5, 6-3, 7-6 (7/3)
Peter Gojowczyk (GER) bt Igor Sijsling (NED) 7-6 (9/7), 2-6, 6-4, 6-1
Lleyton Hewitt (AUS) bt Brian Baker (USA) 6-3, 4-6, 6-3, 6-4
Juan Martn Del Potro (ARG x6) bt Guillermo Garcia-Lopez (ESP) 6-3, 6-7 (5/7), 6-4, 7-6 (9/7)
Andy Murray (GBR x3) bt Michael Llodra (FRA) 6-2, 6-4, 6-3
Leonardo Mayer (ARG) bt Victor Hanescu (ROM) 7-6 (7/4), 6-4, 3-6, 7-6 (7/4)
Andreas Seppi (ITA x20) bt Xavier Malisse (BEL) 6-3, 3-6, 7-5, 7-5
Somdev Devvarman (IND) bt Luks Lacko (SVK) 4-6, 6-1, 6-2, 4-6, 6-4
Stanislas Wawrinka (SUI x9) bt Radek Stepanek (CZE) 7-6 (7/2), 6-3, 6-2
Ivo Karlovic (CRO) bt James Blake (USA) 6-7 (2/7), 3-6, 6-4, 7-6 (7/2), 7-6 (7/2)
Marcos Baghdatis (CYP) bt Go Soeda (JPN) 6-4, 6-3, 6-1
Kevin Anderson (RSA x17) bt Daniel Brands (GER) 7-5, 4-6, 6-2, 6-3
Women's singles
Second round
Jamie Hampton (USA x23) bt Kristina Mladenovic (FRA) 7-5, 6-4
Sloane Stephens (USA x15) bt Urszula Radwanska (POL) 6-1, 6-1
Zheng Jie (CHN) bt Venus Williams (USA) 6-3, 2-6, 7-6 (7/5)
Carla Suarez Navarro (ESP x18) bt Coco Vandeweghe (USA) 6-3, 6-4
Agnieszka Radwanska (POL x3) bt Maria-Teresa Torro-Flor (ESP) 6-0, 7-5
Anastasia Pavlyuchenkova (RUS x32) bt Ashleigh Barty (AUS) 6-4, 6-0
Laura Robson (GBR x30) bt Caroline Garcia (FRA) 6-4, 7-6 (7/5)
Li Na (CHN x5) bt Sofia Arvidsson (SWE) 6-2, 6-2