India clinch women's Test against Australia to end 46 years of hurt
A significant first-innings lead of 187 had put India in the box seat and they needed only 75 runs to clinch the contest after bowling out Australia for 261 in the touring side's second innings.
They lost opener Shafali Verma and number three batter Richa Ghosh, but Smriti Mandhana anchored their chase with an unbeaten 38, sealing India's memorable victory with a four shortly after the lunch break.
The Harmanpreet Kaur-led India had beaten England by 347 runs - the highest victory margin in terms of runs in women's Test cricket - in a one-off test in Navi Mumbai earlier this month.
"It's the reward for all the hard work we have done for so many years," Kaur said after India's first victory against Australia in 11 Tests since the teams first clashed in the longest format in 1977.
"Hopefully after these two wins, we will get to play many more test matches in the upcoming years."
Earlier, India claimed the last five Australian wickets for just 28 runs after the tourists had resumed their second innings on 233-5.
Seamer Pooja Vastrakar trapped Ash Gardner lbw before off-spinner Sneh Rana, who was chosen player of the match for her seven-wicket haul, dismissed Annabel Sutherland (27) and Alana King in successive deliveries.
Left-arm spinner Rajeshwari Gayakwad claimed the last two wickets to hasten Australia's collapse.
"What an amazing experience to come over here and play test cricket," Australia captain Alyssa Healy said.
"It's not easy to win over here, we've found that out. We'd love to play a couple more (tests) to make it really interesting."
The teams will now play three one-dayers and an equal number of T20 Internationals.