India's players celebrate with the trophy after winning the women's Test match against Australia at the Wankhede Stadium in Mumbai on Sunday. AFP

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 offbreak Sneh Rana — later awarded player of the match — taking two wickets in two balls.

India's players applaud the spectators after winning the women's Test match against Australia in Mumbai.  AFP

Set a target of 75, India's skipper Harmanpreet Kaur's team chased down the runs in dramatic play 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 Dec.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."