David Warner and Nathan Lyon put Australia back on track against Bangladesh

Australian cricket captain Steve Smith, left, and his teammate David Warner leave the ground after end of the third day of the first Test against Bangladesh in Dhaka, Bangladesh. AM Ahad / AP Photo

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 captain 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.

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

Tamim led the hosts' batting charge in his 155-ball innings but his dismissal off fast bowler Pat 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 before Smith decided to review.

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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.

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