Virat Kohli blasted 85 but it wasn't enough to prevent Australia from fighting off a T20 series sweep with a thrilling 12-run victory in the final match in Sydney on Tuesday.

While Kohli was at the crease in his imperious 61-ball knock, India had hopes of pulling off victory, but when he fell to a sensational diving outfield catch by Daniel Sams 11 balls from the finish India's hopes went with him.

Before a raucous crowd of over 30,000 -- with attendance limits lifted in new Covid-19 protocols by the New South Wales state government -- Australia set India a competitive 187-run target to chase.

But India could not replicate their dynamic batting at the Sydney Cricket Ground two nights ago when they sealed the T20 series after losing the preceding one-day international series 2-1 to the home side.

"At one stage when Hardik (Pandya) started going we thought we could pull it off," Kohli said.

"The middle over phase during our batting cost us the game. A partnership of 30-odd would've made it easier for Hardik.

"We are finding ways to come back and give the opposition a scare and the series win is a little asterisk for us to finish the 2020 season on a high."

Matthew Wade blasted his highest T20 score and an eventful Glenn Maxwell half-century lifted Australia to 186 for five after India had won the toss.

Maxwell had a night out. He survived two reviews, was caught off a no-ball, had a six prevented by athletic Sanju Samson fielding over the rope and finished with three sixes before he was out for 54 off 36 balls.

Wade put on 90 with Maxwell for the third wicket before he was leg before wicket to Shardul Thakur for 80 -- his highest T20 score -- off 53 balls with seven fours and two sixes.

"It was a great series, and we just happened to be on the wrong end of the first two," Australia captain Aaron Finch said.

"It's the first time in a T20 series we've had two leg-spinners in the side, and they were bold with the short boundaries here, so credit to both of them."

Swepson shines

Maxwell was given the new ball and got KL Rahul's wicket with his second delivery in India's innings, hitting down the throat of Steve Smith at deep mid-wicket.

But Smith put down a similar catch when Kohli was on nine in Maxwell's next over in what could have been a major turning point.

Sams took a superb diving catch at the second grab in the deep to dismiss Shikhar Dhawan for 28 off leg-spinner Mitchell Swepson in the sixth over.

Smith made amends for his earlier costly fumble to catch Samson for 10 off Swepson and then pulled off an incredible leap over the ropes to prevent a six off Kohli next ball.

Swepson finished his final over with the wicket of Shreyas Iyer, lbw for a first-ball duck to finish with three for 23. He was named man-of-the-match.

Sams had 20 runs taken off his second over, two sixes by Kohli and another one from Pandya to rev up India's run-rate.

India needed 43 runs off the last three overs to win, but leg-spinner Adam Zampa crucially removed Pandya for 20, caught by Finch.

Pandya was subsequently named man of the series for his match-winning innings to guide India to a series win in the second T20 on Sunday.

"After the 2nd ODI we thought we'd think of this as a four-match series and we managed to get three wins, so we're happy with that," Pandya said.

Sams took another super diving catch to finish Kohli's innings and India's hopes off Andrew Tye in the penultimate over.