Virat Kohli said it was "very special" to lead India to their first Test win in Australia for a decade which gave his side crucial momentum in their bid for a maiden series victory.
The visitors won a close contest in Adelaide by 31 runs on the fifth day after setting Australia a target of 323.
It was a big breakthrough for Kohli's men, with their last triumph on Australian soil at the WACA Ground in Perth in 2008. In Adelaide, their sole previous win was in 2003.
"Obviously it's a great feeling. We've never taken a lead in a series in Australia, something that for us is a huge boost," he said.
"And it's given us the right momentum that we needed to play a big series like this and it's something that we've had to work hard for.
"Any Test victory is special because you work hard over five days, and then the physical and the mental toil and the emotion of it all comes together in a result is a very special feeling."
Kohli said he believed his team collectively were better than Australia and deserved to win.
The victory was built on Cheteshwar Pujara's gritty 123 and 71 in both innings while wicketkeeper Rishabh Pant took a world record-equalling 11 catches.
Rishabh Pant grabbed 11 catches in the first Test against Australia at Adelaide – the most in the format for India ??— Cricingif (@_cricingif) December 10, 2018
He also equalled the all-time record of Jack Russell and AB de Villiers ?? #AUSvIND pic.twitter.com/XVKF9qiEdF
"It was priceless from Pujara, we were down and out at lunch on day one. His grit and determination brought us back in it," said Kohli.
"We always knew that runs on the board would make the home side tentative. Any lead was gold and we got 15. In the second innings again, he and Rahane batted well."