Chasing 162 for victory in the final innings, Australia stumbled early losing 3-19 before Beau Webster finished a perfect debut by completing the six-wicket victory.
The result completed a 3-1 series triumph for Australia over one of their closest rivals, with the Sydney win coming on the back of unsung heroes such as Scott Boland and Webster.
Travis Head was unbeaten on 34, after an impressive series with the bat. (Dan Himbrechts/AAP PHOTOS)
Flogged by 295 runs in the first Test in Perth, the victory marked the first time Australia had come from behind to win a five-Test series since the 1997 Ashes.
Realistically, only rain in Brisbane stopped Australia from winning all four remaining Tests after that series-opening defeat, with the hosts asserting their dominance after early criticism.
And the revival couldn't have come at a better time for Cummins and several of his teammates; Alex Carey, Usman Khawaja and Travis Head were among other Test mainstays never to have tasted a series victory over India.
"Unreal. This was one a few of us didn't have," Cummins said.
"It's been an amazing series. It's one of those that's been in the calendar for a fair while, always got an eye on it for the last year or two.
"It's really It's lived up to all the hype."
Scott Boland was a hero for Australia, taking 6-47 to finish with 10 wickets at the SCG. (Dan Himbrechts/AAP PHOTOS)
Australia's win also wrapped up their spot in June's World Test Championship final against South Africa at Lord's, regardless of the outcome of the looming two-Test tour of Sri Lanka.
But the more remarkable feat is where Cummins' side has come from in recent years.
When India toured Australia six summers ago and beat the hosts 2-1, Australia was a side in crisis still reeling from the ball-tampering scandal.
In the six years since, Australia have either won or drawn 14 of the 16 series they have played, while also lifting the World Test Championship in 2023.
Sunday's victory ensured Cummins' side own every bilateral trophy in Test cricket, the first time Australia has done so since 2008.
That alone puts the team among the greats, along with their status as current Test and one-day world champions.
Beau Webster finishes it off and Australia claims the Border-Gavaskar Trophy! — cricket.com.au (@cricketcomau) #AUSvIND | #PlayOfTheDay | @nrmainsurance pic.twitter.com/fl5tmIMPPdJanuary 5, 2025
"I didn't know we'd won everything until half hour ago, but that's always the aim," Cummins said.
"One of the things I love most about Test cricket is it challenges you in so many ways.
"You need an amazing squad, amazing support staff to be able to win everywhere in the world. And I think that's what we've been able to do.
"That consistency over a few years to do that with a very similar squad has been massive."
Winning did not come easy for Australia at the SCG, on the most lively wicket the ground has had this century.
Boland was immense, taking 10 wickets for the match, including 6-45 in India's second innings of 157 just as the tourists looked ready to set a difficult target.
At age 35, the Victorian is the oldest quick in Australia's team, but carried the load in Sydney in the best performance of his career.
Then when Australia wobbled with the bat, the team's senior statesman Khawaja held the innings together.
Beau Webster (r) and Travis Head were unbeaten at the finish after their match-winning partnership. (Dan Himbrechts/AAP PHOTOS)
With India's chief tormentor Jasprit Bumrah nursing a sore back and unable to bowl, Sam Konstas breathed fire early with 22 from 17 balls.
But Australia went from 0-39 in the fourth over to 3-58 shortly after when Konstas, Marnus Labuschagne and Steve Smith all fell to Prasidh Krishna.
Smith's wicket was particularly frustrating, leaving him stranded on 9999 Test runs when he edged off to the quick.
From there, Khawaja stabilised alongside Travis Head in a vital 46-run partnership that broke the back of the chase.
Khawaja was eventually caught behind on 41, but there was to be no last sting in the tail as Webster (39no) backed-up his first-innings half century to help Head (34no) steer Australia to an era-defining victory.
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