Australia has won the Border-Gavaskar Trophy with a thrilling victory over India in the Sydney Test, a fitting end to one of the best series ever seen on these shores.

India were bowled out for 157 early on day three, setting the hosts 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 Rishabh Pant, with Siraj claiming his first scalp.

Out marched Beau Webster on debut, the towering Tasmanian 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 at 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.

Scott Boland was named Player of the Match for his 10 wickets in Sydney, while Bumrah was named Player of the Series.

But it was Webster who hit the winning runs at the SCG, capping off a dream debut for the 31-year-old.

Webster now looks likely to add to his Test caps on the two-match tour of Sri Lanka, which first-choice allrounder Cameron Green will again miss through injury.

An announcement on the Test team is expected in the days after the SCG Test finishes, given the first Test begins in Galle on January 29.

“There’s a discussion coming up,” McDonald said when asked of Webster’s selection chances.

“(Chief selector) George Bailey will sit down and look at that Sri Lankan squad at the end of this Test match and there’ll be a quick turnaround to the announcement.

“He’s put his best foot forward. Our angle is that he’s up to the level, we wouldn’t have picked him if he wasn’t.

“It gives us another all-round option. To have depth in that area bodes well for us as a team and for Beau also.”