India pulled off a record run-chase in a thrilling final session to hand Australia their first defeat at Brisbane's Gabba ground since 1988 and clinch the four-Test series 2-1 on Tuesday.
Wicketkeeper Rishabh Pant starred with a swashbuckling 89 not out as the injury-depleted visitors overhauled the 328-run target with three overs to go, winning by three wickets.
Australia had not been beaten at the Gabba since falling to Viv Richards' all-conquering West Indies side by nine wickets in November 1988.
India's 329 for seven also smashed the 69-year-old record for the biggest run-chase at the Gabba, set by Australia, who scored 236 for seven to beat the West Indies in 1951.
The series win was a remarkable achievement considering India were bowled out for their lowest Test score of 36 to lose the first Test in Adelaide, before bouncing back to win the second in Melbourne.
The visitors, ravaged by injuries and captain Virat Kohli's absence for paternity leave, then batted throughout the final day to draw the third Test in Sydney.
"It really means a lot to us. I don't know how to describe this victory but I'm really proud of all the boys," said India's interim skipper Ajinkya Rahane.
"They showed character, attitude, especially after the Adelaide Test match. We decided we're going to fight really hard... and we just wanted to give our best."
Man-of-the-match Pant, who played a similar innings in the drawn Sydney Test, blasted his 89 from 138 balls with nine fours and a six.
His innings followed an equally impressive knock from 21-year-old Shubman Gill, who made 91 at the top of the order earlier in the day.
'Completely outplayed'
Cheteshwar Pujara's 56 was also vital, the gritty number three hit 10 times by Australia's quicks, taking blows to the fingers, arm, ribs and head as he was subjected to a searching examination by Pat Cummins and Josh Hazlewood.
Cummins with 4-55 was easily the pick of the Australian attack, sending down 24 overs of pace and hostility, but the rest of the bowlers looked fatigued after bowling all day in Sydney just eight days ago.
"I'm absolutely disappointed, no doubt about that. We've come here to win the Test and win the series," said Australia captain Tim Paine.
"It's probably a little bit of a trend the whole series -- I think in the key moments we were found wanting and completely outplayed by a really disciplined, really tough Indian side who fully deserved the series win."
Despite Australia's fearsome record at the Gabba, the Indian batsmen showed no fear and never looked interested in playing for a draw, even after losing the wickets of Pujara and Mayank Agarwal after tea.
Pant took advantage of any loose ball, but also played some outrageous strokes, showing the influence T20 cricket has had on Tests.