Azarenka, 19, broke six of Mauresmo's nine service games as she cruised to victory in 87 minutes.
The 13th seed won her first WTA singles title at the Brisbane International this month and faces world number two Serena Williams in the fourth round on Monday.
Mauresmo went into the tournament under an injury cloud after straining her left thigh in a warmup event in Brisbane.
She pulled out of the Sydney International but recovered to take her pace at Melbourne, although she was short of confidence coming in.
"It's a little bit frustrating to come out with only six games today but I did not play well enough on the key points," Mauresmo said.
"In the first set, I had the lead early on, but was not able to really keep it up. Then in the second set, I was down but also had opportunities to close the gap a little bit."
Despite her defeat, Mauresmo, now one of the older players on the women's WTA Tour, said there were penty of positives she could take out of her performances in Australia.
"Even though it's now quite disappointing, I think my (best) level of play is coming back. It's slowly getting there," she said.
"I have to be a little bit patient I guess with the things we worked on in the winter. Some things are good, some other things are still up and down."
OneIndia News (With inputs from Agencies)