Australian captain Tim Paine has urged his side to dream of Dubai as they look to pull off a record-breaking victory against India in Adelaide on Monday.

Almost two months on from Australia’s great escape against Pakistan in the UAE, Paine’s young team face an equally daunting task against the world’s number one Test side, needing 219 runs to beat India on Monday with six wickets in hand.

If Australia are able to pull off their pursuit of 323 to win, it would be the highest-successful run chase ever in an Adelaide Test, eclipsing the current record of 6-315 set at the turn of the 20th Century.

With the Dubai Test still fresh in the memory, when Usman Khawaja, Travis Head and Paine helped the Aussies bat out almost 140 overs and secure a draw, the young Australian side are daring to believe despite history being against them.

"Tim was just saying that we’ve had that belief before when our backs have been against the wall," spinner Nathan Lyon said after the hosts finished day four on 4-104.

"We’ve got a massive sniff here, I believe.

"We still believe we can win this.

"It’s about coming out tomorrow and winning the first ball, the first over, the first hour and just breaking it down. Cricket’s a very simple game and we just need to not complicate things and enjoy ourselves."

Lyon also backed South Australian skipper Head to "make a hero of himself on his home ground" by scoring his maiden Test century on Monday and steering his side to victory.

Head impressed in scoring 72 on debut in that fourth innings of the Dubai Test, a score he matched in the first innings here.

Much of the responsibility on Monday will fall on Head, who will resume on 11 not out in just his third Test, and veteran Shaun Marsh (31no), who scored an unbeaten 163 to steer Western Australia to victory in a JLT Sheffield Shield game in Adelaide last month.

Head received warm applause from his home fans when he walked to the crease on Sunday and Lyon, who presented the left-hander with his Baggy Green cap in Dubai, has backed the 24-year-old to produce the goods.

"There’s a chance for Travis Head to come out a make a hero of himself on his home ground," Lyon said.

"Everyone knows that I’m close with Travis and I’m a big fan of him.

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"Both of those guys have my full support and I guarantee that whole change room is right behind those guys out there.

"I think the pitch has quickened up a little bit and is doing a lot less for the seamers.

"It's definitely spinning, and they've got a world-class spinner, so it's going to be a great challenge for … two left-handers, with Ravi (Ashwin) spinning it away.

"But the wicket's good enough for us to really knuckle down tomorrow and have the belief we can score these runs."