Victory was enough to ensure they will defend their World Test Championship title in the June final at Lord’s in England against South Africa.
It culminated in a thrilling tour full of twists and turns that saw record crowds and some spectacular individual performances.
The five-test series witnessed the emergence of exciting young talent in the form of Australian opener Sam Konstas and Indian all-rounder Nitish Kumar Reddy.
At the same time, ageing veterans, notably Rohit Sharma, showed that the clock is ticking on their careers.
India won the first match in Perth convincingly before Australia bounced back in the day-night affair at Adelaide.
The rain-hit Brisbane clash ended in a draw before the hosts took all the momentum into Sydney with a pulsating day-five win in Melbourne.
Indian pace spearhead and skipper Bumrah, who has been dealing with a back issue, batted briefly when his team resumed after bowling just one over and leaving the field on Saturday.
But in a huge setback the 31-year-old did not appear again, leaving Mohammed Siraj and Prasidh Krishna to lead the bowling attack, with Virat Kohli in charge.
It appeared to be a difficult run chase on a deteriorating surface offering plenty for the bowlers, but Konstas and Khawaja had other ideas.
They raced to 35 off the first three overs, with teenager Konstas hitting out.
It proved his downfall, unnecessarily lashing at a good length ball from Prasidh only to sky it to Washington Sundar at mid-off, out for 22.
Prasidh then knocked over Marnus Labuschagne for six, caught by Yashasvi Jaiswal at slip, with the same pair removing Smith on four, fending off a rising ball.
Veteran Khawaja, who had a poor series, produced some cracking boundaries on his way to 41, but he mistimed a pull shot off Siraj with wicketkeeper Rishabh Pant collecting the edge.
It gave India a glimmer of hope before Head and Webster took the game away.
India resumed after a counter-attacking 61 from Pant helped build their second-innings lead.
Ravindra Jadeja began on eight and Sundar on six after they dismissed Australia for 181 in reply to their first-innings 185.
Jadeja crunched an early boundary off Pat Cummins, but he was out two balls later, getting a faint nick to wicketkeeper Alex Carey, adding just five to his overnight score.
The Australian skipper struck again to bowl Sundar for 12.
That brought Bumrah to the crease and he could only watch as Siraj edged Boland to Khawaja at slip to give the big Australian his fifth wicket.
Boland, whose line and length were impeccable all series, then bowled Bumrah to end the innings.
