Resuming at four for none on the final day, India overhauled the target with 18 balls to spare in a match that went down to the wire.
Rishabh Pant led the chase with his aggressive yet mature unbeaten 89 while Shubman Gill scored 91.
Cheteshwar Pujara endured many painful blows on his body in his dogged 56-run knock that he raised with a 211-ball vigil.
We are all overjoyed at the success of the Indian Cricket Team in Australia. Their remarkable energy and passion wa… https://t.co/SJXTJwpgEm
— Narendra Modi (@narendramodi) 1611042538000
Australia had won the pink-ball Adelaide Test while India struck back with victory in Melbourne. The third Test in Sydney had ended in a draw.
India had won a historic Test series Down Under two years back and now the team is cherishing back-to-back series victory.
Victory scenes at the Gabba.#AUSvIND https://t.co/Z5nB9MyPwh
— BCCI (@BCCI) 1611042645000
The visitors had lost the ODI series before winning the T20 series that preceded the Test rubber.
At the start, India lost experienced vice captain Rohit Sharma (7) early but young Gill rose to the occasion with an impressive knock that kept India in the hunt as Pujara dug heels on the other end.
Rahane did try to build on the good start with his short but attacking 24-run knock before his sift dismissal.
With Pant’s ability to strike the ball at brisk pace, India always had a chance to get for the kill.
Pant pulled off some breathtaking cover drives off Pat Cummins and Josh Hazlewood in the final session though he benefited from a missed stumping chance.