Azarenka remained unbeaten in 2013, having successfully defended her Australian Open title and her WTA Doha crown.
The 23-year-old from Belarus, currently ranked second in the world behind American Serena Williams, is vying to become the first woman to win back-to-back titles at Indian Wells since Martina Navratilova in 1990 and 1991.
In the round of 16 she'll face Poland's Urszula Radwanska, a 6-0, 7-6 (7/4) winner over American Jamie Hampton.
Results on Monday from the sixth day of the ATP Masters and WTA BNP Paribas Open (x denotes seeded player):
Men
Third round
Kevin Anderson (RSA) bt Jarkko Nieminen (FIN) 6-3, 6-1
Rafael Nadal (ESP x5) bt Leonardo Mayer (ARG) walkover
Ernests Gulbis (LAT) bt Andreas Seppi (ITA x20) 5-7, 6-3, 6-4
Tomas Berdych (CZE x6) bt Florian Mayer (GER x27) 6-4, 6-1
Roger Federer (SUI x2) bt Ivan Dodig (CRO) 6-3, 6-1
Richard Gasquet (FRA x10) bt Jerzy Janowicz (POL x24) 6-1, 6-4
Gilles Simon (FRA x13) bt Benoit Paire (FRA) 3-6, 7-6 (7/5), 6-4
Stanislas Wawrinka (SUI x18) bt Lleyton Hewitt (AUS) 6-4, 7-5
Women
Third round
Angelique Kerber (GER x4) bt Yanina Wickmayer (BEL x30) 6-1, 7-6 (7/4)
Garbine Muguruza (ESP) bt Magdalena Rybarikova (SVK) 6-4, 6-0
Nadia Petrova (RUS x10) bt Julia Goerges (GER x21) 6-1, 6-2
Samantha Stosur (AUS x7) bt Peng Shuai (CHN x32) 6-3, 3-6, 6-2
Caroline Wozniacki (DEN x8) bt Elena Vesnina (RUS x29) 6-2, 6-1
Mona Barthel (GER x24) bt Ana Ivanovic (SRB x11) 6-1, 3-6, 6-0
Victoria Azarenka (BLR x1) bt Kirsten Flipkens (BEL x28) 3-6, 6-3, 6-0
Urszula Radwanska (POL) bt Jamie Hampton (USA) 6-0, 7-6 (7/4)