The Indo-Croatian duo defeated the Pak-Kazakhstani team 7-5 and 6-2 on Tuesday.
Mirza with her mixed doubles partner scored 23 winners in the match and had 16 unforced errors to their name compared to their opponents’ 27 winners and 20 unforced errors.
They will now face India’s Leander Paes and Martina Hingis of Switzerland.
On the other hand, Mirza and Martina Hingis progressed to the next stage of Australian Open’s women’s doubles category.
They defeated German-American team of Anna-Lena Groenefeld and Coco Vandeweghe 6-2 4-6 and 6-1.
Mirza and Hingis hit 22 winners and had 16 unforced errors in comparison to their opponents 16 and 25 unforced errors.