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Anderson, the 14th seed, defeated Ricardas Berankis of Lithuania in straight sets on Wednesday.
The South African No 1 had no trouble, winning 6-2, 6-2, 7-6 (7/3) to set up a third round encounter with 24th seeded Frenchman Richard Gasquet.
Gasquet beat local hope James Duckworth of Australia 6-2, 6-3, 7-5.
Results from day three of the Australian Open at Melbourne Park on Wednesday:
Men's singles
Second round
Tomas Berdych (CZE x7) bt Jurgen Melzer (AUT) 7-6 (7/0), 6-2, 6-2
Viktor Troicki (SRB) bt Leonardo Mayer (ARG x26) 6-4, 4-6, 6-4, 6-0
Marcos Baghdatis (CYR) bt David Goffin (BEL x20) 6-1, 6-4, 4-6, 6-0
Kevin Anderson (RSA x14) bt Ricardas Berankis (LTU) 6-2, 6-2, 7-6 (7/3)
Andy Murray (GBR x6) bt Marinko Matosevic (AUS) 6-1, 6-3, 6-2
Joao Sousa (POR) bt Martin Klizan (SVK x32) 4-6, 7-6 (7/4), 6-4, 1-0 retired
Richard Gasquet (FRA x24) bt James Duckworth (AUS) 6-2, 6-3, 7-5
Roger Federer (SUI x2) bt Simone Bolelli (ITA) 3-6, 6-3, 6-2, 6-2
Grigor Dimitrov (BUL x10) bt Lukas Lacko (SVK) 6-3, 6-7 (10/12), 6-3, 6-3
Andreas Seppi (ITA) bt Jeremy Chardy (FRA x29) 7-5, 3-6, 6-2, 6-1
Women's singles
Second round
Carina Witthoeft (GER) bt Christina McHale (USA) 6-3, 6-0
Peng Shuai (CHN x21) bt Magdalena Rybarikova (SVK) 6-1, 6-1
Ekaterina Makarova (RUS x10) bt Roberta Vinci (ITA) 6-2, 6-4
Yaroslava Shvedova (KAZ) bt Monica Puig (PUR) 6-2, 7-6 (8/6)
Julia Goerges (GER) bt Klara Koukalova (CZE) 6-3, 4-6, 6-2
Irina-Camelia Begu (ROU) bt Katerina Siniakova (CZE) 7-5, 6-4
Lucie Hradecka (CZE) bt Polona Hercog (SLO) 4-6, 6-3, 6-2
Karolina Pliskova (CZE x22) bt Oceane Dodin (FRA) 7-5, 5-7, 6-4
Maria Sharapova (RUS x2) bt Alexandra Panova (RUS) 6-1, 4-6, 7-5
Yanina Wickmayer (BEL) bt Lara Arruabarrena (ESP) 6-4, 4-6, 6-4
Sara Errani (ITA x14) bt Silvia Soler-Espinosa (ESP) 7-6 (7/3), 6-3
Caroline Garcia (FRA) bt Stefanie Voegele (SUI) 6-3, 6-4
Zarina Diyas (KAZ x31) bt Anna Schmiedlova (SVK) 3-6, 6-2, 8-6
