Australia have won the Border-Gavaskar Trophy with a thrilling victory over India in the SCG Test in a fitting end to one of the best series ever seen on Aussie soil.

After India were bowled out for 157 early on day three, the hosts were set a fourth-innings run chase of 162.

Without the firepower of superstar quick Jasprit Bumrah, who did bat but did not bowl due to back spasms, the visitors were forced to rely on Mohammed Siraj and Pradish Krishna to take 10 wickets.

Krishna stuck early, dismissing teenage sensation Sam Konstas in the fourth over as he skied it but not before the fearless opener sliced 22 runs of the total.

Marnus Labuschagne was the next to fall for just six runs, as the No.3 guided a Krishna delivery to Yashasvi Jaiswal in the gully.

Steve Smith was caught one run shy of becoming the fourth Australian to reach 10,000 Test runs, as with Jaiswal taking another in the fully off Krishna.

Having got himself settled in with a front row seat to the Konstas show, veteran opener Usman Khawaja looked the best he has all series as he moved to 41.

On a spicy SCG wicket, Khawaja attempted a pull shot but it struck the bottom edge and was caught behind by Rishahb Pant, with Siraj claiming his first scalp.

Out marched Beau Webster on debut, the towering all-rounder fresh off a 57 in the opening dig.

As the total shrunk, the Indian bowlers got more and more desperate for wickets, which opened up scoring opportunities for Webster and Travis Head.

The pair smelt blood and went on the attack, finding the rope as they went as almost a run-a-ball.

With four runs needed for victory in the fifth Test, Webster found the boundary again in a fitting finish as Australia won the series 3-1.