Azarenka needed just 67 minutes to beat the West Australian 6-3 6-1 at Pat Rafter Arena on Wednesday night and move into a quarter-final against Swiss Stefanie Voegele.
The 24-year-old from Belarus, making her first appearance on Australian soil since being jeered on court at last year's Australian Open final, was imperious as she eliminated Dellacqua, the last Australian in the women's draw following Ashleigh Barty's injury-enforced withdrawal on Tuesday.
After breaking Dellacqua in the sixth game of the first set, Azarenka applied the blowtorch in the second.
The two-time Australian Open winner broke Dellacqua in the first game of the second set before pulling clear to a 5-0 lead.
Dellacqua managed to save a match point before breaking Azarenka but it was a stay of execution as the Belarusian responded to close out the match in the next game and move into the last eight.
In Wednesday's other action, German fifth seed Angelique Kerber moved into the quarter-finals after Russian Anastasia Pavlyuchenkova retired injured in their second round clash.
World No.9 Kerber led 6-2 4-3 before last year's Brisbane finalist Pavlyuchenkova succumbed to a leg complaint.
Pavlyuchenkova - the world No.26 - took a medical timeout to have her left leg strapped trailing 3-2 in the second set before lasting just two more games.
Two-time grand slam semi-finalist Kerber booked a quarter-final clash with former world No.1 Jelena Jankovic.
Pavlyuchenkova's injury followed the withdrawal of Wimbledon finalist Sabine Lisicki (illness) from her second round clash with Voegele on Wednesday.
Officials confirmed that the world No.15 and German seventh seed was suffering a gastrointestinal illness.
It was another blow to the women's draw which lost Barty (adductor) before her second round showdown with four-time grand slam winner Sharapova.
The world No.4 will next play 2012 Brisbane finalist Kaia Kanepi in a quarter-final match at Pat Rafter Arena on Thursday before top seed and world No.1 Williams takes on Dominika Cibulkova for a spot in the semis.
Azarenka said she was just happy to finally kickstart her summer and the form of Williams, Sharapova and likely semi-final opponent Jelena Jankovic so far was of no concern to her.
"I don't really care until I really play somebody like Jelena," she said.
"You cannot underestimate any opponent in the draw ever, in any tournament, because we've seen a lot of surprises.
"If you underestimate, you can just lose your focus. I always try to put my opponent as a 50/50 when we go on the court and just try to be better that particular day."
One thing that had caught Azarenka's attention was the news former world No.1 Caroline Wozniacki had got engaged to golfer Rory McIlroy in Sydney on New Year's Eve.
"I saw the news, and I got to say I'm really happy for her," Azarenka said.
"If she will remember, and I don't know if she will, I called it last year when I saw her in the locker room (in Brisbane). I said, `you'll be engaged by the end of the year'. Technically, I was right."