David Warner scored an unbeaten half-century to steady Australia as they chased a challenging victory target in the first Test against Bangladesh in Dhaka on Tuesday.

Warner, who remained unbeaten on 75, scored the bulk of the runs as the visitors advanced to 109-2 at stumps on the third day, still needing another 156 for victory.

Nathan Lyon earlier claimed 6-82 to dismiss Bangladesh for a modest 221 in their second innings and give Australia a scent of victory.

Bangladesh looked confident when spinner Mehedi Hasan trapped Matt Renshaw leg-before for five and Usman Khawaja hoisted a catch to Taijul Islam at square leg off Shakib al Hasan in the next over.

Australia, teetering on 28-2, nearly lost another wicket when skipper Steve Smith appeared to have been stumped off Mehedi and walked.

But he was called back after replays showed his feet had dragged slightly behind the crease as wicketkeeper Mushfiqur Rahim broke the stumps.

Smith was dropped again by Imrul Kayes off Mehedi on three. He went on to score 25 not out and put on an undefeated 81 with Warner for the third wicket.

Warner, who faced 96 balls and hit 11 fours and a six, also had his share of luck when he was dropped by Soumya Sarkar on 14 off Shakib.

Paceman Pat Cummins said Warner's strong showing would inspire the remaining batsmen.

"He was so focused," said Cummins.

"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."

Earlier, Lyon took full advantage of a spinning track at the Sher-e-Bangla National Stadium to halt Bangladesh's progress.

Tamim led the charge with his 155-ball innings but his dismissal off Cummins for 78 triggered a collapse.

The left-hander fell to a short ball that whistled past him. Umpire Aleem Dar turned down a muted appeal from the bowler but Smith decided to review.

Replays suggested the ball had brushed Tamim's gloves, ending a fine innings which included eight fours to follow his 71 in the first innings.

Shakib was next out for five, hoisting a catch to Cummins at extra cover off Lyon. But Mushfiqur Rahim stayed calm until an unfortunate run out for 41 at the non-striker's end.

Lyon removed Nasir Hossain (0) and Ashton Agar sent back Sabbir Rahman (22), dragging the hosts down further.

But Tamim was still confident the hosts could secure victory.

"The wicket is unpredictable, anything can happen. We have to be patient because one wicket has brought two or three in a cluster. We can bowl better than we did today," he said.

Bangladesh, ranked a lowly ninth in Tests, are seeking their first-ever win over fourth-placed Australia in what is only the fifth Test meeting between the two teams.