The Belarusian, who will defend her title in Melbourne when the first Grand Slam of the year starts on January 14, was simply too good for her Kazak opponent, who wilted in the Queensland heat.
Azarenka registered a bagel in the opening set before dropping just one game in the second to secure the most comprehensive of victories and set up a semi-final date with Serena Williams.
The number three seed beat compatriot Sloane Stephens 6-4 6-3 in an all-American clash, the last women's encounter of the day.
Serena beat her good friend in 72 minutes with ruthless efficiency, winning 84 per cent of the points on her first serve, and broke with each of her two opportunities.
In the other half of the draw, Anastasia Pavlyuchenkova will play Lesia Tsurenko for a place in the final.
Russian Pavlyuchenkova shocked fourth seed Angelique Kerber of Germany 7-6(3) 7-6(3) while Ukrainian Tsurenko downed Daniela Hantuchova of Slovakia 6-3 6-4.
WTA Brisbane results
1-Victoria Azarenka (Belarus) beat Ksenia Pervak (Kazakhstan) 6-1 6-0
3-Serena Williams (U.S.) beat Sloane Stephens (U.S.) 6-4 6-3
Anastasia Pavlyuchenkova (Russia) beat 4-Angelique Kerber (Germany) 7-6(3) 7-6(3)
Lesia Tsurenko (Ukraine) beat Daniela Hantuchova (Slovakia) 6-3 6-4
WTA Auckland results
1-Agnieszka Radwanska (Poland) beat Elena Vesnina (Russia) 6-3 6-3
3-Yanina Wickmayer (Belgium) beat Kirsten Flipkens (Belgium) 6-3 6-4
8-Mona Barthel (Germany) beat Johanna Larsson (Sweden) 6-2 6-1
Jamie Hampton (U.S.) beat Kiki Bertens (Netherlands) 6-1 6-7(5) 6-2
WTA Shenzhen results
1-Li Na (China) beat 8-Bojana Jovanovski (Serbia) 6-3 6-3
5-Klara Zakopalova (Czech Republic) beat 2-Marion Bartoli (France) 6-3 6-2
6-Peng Shuai (China) beat Annika Beck (Germany) 2-6 7-5 6-2