The Belarusian, who was given a bye in the first round, proved too strong for the 2011 Wimbledon finalist as she recorded a 6-3 6-3 result.
The win takes reigning Australian Open champion Azarenka through to the quarter-finals and a meeting with Ksenia Pervak.
Fourth seed Angelique Kerber survived a first-set scare to book her place in the last eight, beating Monica Puig 3-6 6-4 7-6 (9/7).
Sloane Stephens also won her second-round encounter against Sofia Arvidsson, 6-3 6-4, while Lesia Tsurenko saw off home favourite Jarmila Gajdosova 1-6 6-1 6-4.
In the men's second round, third seed Gilles Simone needed tie-breaks to overcome the challenge of Colombian Alejandro Falla, prevailing 7-6 (7/5) 7-6 (7/5).
Fifth seed Kei Nishikori enjoyed a more straightforward 6-3 6-3 win over Tommy Robredo but Florian Mayer, seeded sixth, saw his tournament ended with a 6-4 6-2 loss to Marcos Baghdatis.
Alexandr Dolgopolov also progressed when his opponent Jarkko Nieminen retired through illness. The fourth seed was leading 6-2 4-1 at the time.