India's women's cricket team cruised to their first-ever win against Australia in Tests Sunday, beating the visitors by eight wickets in a one-off match in Mumbai.

India dominated play in the four-day match at the Wankhede Stadium, smashing 406 runs in the first innings to take a 187-run lead.

On the final day, Australia knocked out 261, with India's bowlers earning five wickets for just 28 runs, including right arm off-break Sneh Rana -- later awarded player of the match -- taking two wickets in two balls.

Set a target of 75, India's skipper Harmanpreet Kaur's team chased down the runs in just under 19 overs for two wickets.

For India's women, it was their first Test victory against Australia after 11 attempts since 1977.

It follows India's victory against England last week, also in Mumbai.

Jay Shah, the Board of Control for Cricket in India secretary, celebrated the back-to-back Test wins.

"They conquered it with brilliance," Shah posted on social media, praising skipper Harmanpreet Kaur. "History made today!"

India on December 16 thrashed England by 347 runs in another one-off women's Test, their first ever win at home against the rivals.

India's victory margin against England was the largest by runs in women's Test cricket and also their first Test win against England at home.

"Everything went very well for us," Kaur told reporters on Sunday.

"Hopefully after these two wins we will get many more Test games in upcoming games."