The duo shared the opening two sets, before world number one Azarenka came out on top in a final-set tie-break.
Reflecting on the match, Azarenka was full of praise for the way that the defending champion performed.
"I think she played amazing, so much higher the level was today," Azarenka told reporters.
"She made me play my best tennis. She kept hitting the lines, making those first serves. I kept saying, 'Miss, miss,' but she didn't."
Azarenka has one Grand Slam title to her name, having won the Australian Open earlier this year.