David Warner leads Australia back from the brink in first test against Bangladesh

David Warner has buried his subcontinent demons to give Australia the chance to pull off a miracle win over Bangladesh in the first Test in Dhaka.

Set 265 for victory, Warner scored an unbeaten 75 to lift the visitors to 2-109 at stumps on day three.

Skipper Steve Smith, who survived a tight stumping decision from his first ball, reached 25 not out, leaving Australia needing a further 156 runs to pull off an unlikely triumph.

Warner's struggles on the subcontinent have been a major headache for Australia but he dug deep on Tuesday to produce his second-highest Test score in Asia.

The vice-captain played with aggression and confidence, cracking 11 fours and a six in an innings lauded by Australian quick Pat Cummins.

"He's such a big player for us, and you could just see it in his eye when he was out there - he was so focused," Cummins said.

"We always say 'be the bull' and he looked like he was the bull out there, just focused and taking the game on.

"He got his 50 rapidly, and I think it just changes the whole momentum but also the mindset for the other batsmen who are to come in, just taking the game on."

If Australia succeed in their imposing run-chase, it will be their second-highest fourth-innings run chase in Asia.

Not since Ricky Ponting guided his team to a target of 307 against Bangladesh in nearby Fatullah in 2006 has Australia scaled such heights in the region.

Perhaps the most treacherous element that stands in Australia's way is a deteriorating pitch that will only get harder to bat on.

Such a fightback had looked far from likely when Matt Renshaw and Usman Khawaja both fell cheaply.

After playing the spin with confidence during his first-innings of 45, Renshaw looked far less assured the second time around and was trapped lbw by offspinner Mehedi Hasan on five.

Khawaja (one) continued his disastrous return to national duties, lofting a sweep shot to Taijul Islam at deep backward square leg off Shakib Al Hasan's left-arm spin.

Warner was given a life by a Bangladeshi side that earlier in the day had been deserved favourites to claim their maiden Test victory over Australia.

Warner's cut shot found his edge but Soumya Sarkar couldn't secure a tough catch at first slip, while Smith was later dropped by Imrul Kayes at short leg.

Nathan Lyon earlier spun Australia back into contention with 6-82 as Bangladesh were bowled out for 221 shortly after tea.

The tourists looked in serious trouble after losing Josh Hazlewood to a side strain within the first hour of the morning session.

Hazlewood will return home at the conclusion of the first Test and will also miss next month's limited-overs tour of India.

Lyon was the pick of the bowlers, while Ashton Agar snared 2-55 and Cummins 1-38.