Australian Open champion Azarenka won 6-2 6-3 to move into the third round after receiving a bye in the first round.
The Belarussian's world number one spot is under threat at the $2.3 million event where American Serena Williams and Russian Maria Sharapova can reclaim top spot.
Fifteen-times grand slam champion Williams will return to the top of the rankings for the first time since 2010 if she makes the semi-finals, while Sharapova could become number one if she wins the title.
Both won their second-round matches on Tuesday.
Playing her first match since retaining the Australian Open, Azarenka dropped her opening service game but once she found her range she had too much firepower for Swiss Oprandi.
Azarenka will next play American Christina McHale who knocked out Lucie Safarova.
Fourth seed Agnieszka Radwanska also moved safely through to the third round with a 6-3 6-2 defeat of Australia's Anastasia Rodionova while former world number one Caroline Wozniacki faced some stiff resistance initially from Sorana Cirstea before winning 7-6 6-0.
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