The visitors are only 80 runs behind and have eight first innings wicket in hand after the close of second day's play.
Warner who, scored brilliant hundred in the first Test, once again was in sublime form as he seems destined for another century with gritty unbeaten 88 runs along with Handscom with responsible 69 runs were at the crease when the stumps were drawn for the day.
The big hitting opener Warner first added 93-run second wicket stand with his skipper Steven Smith and then again paired another unbeaten 127-run as Australia finished the second day on top.
Australian skipper Steven Smith scored a defiant 58 before being clean bowled by Taijul Islam on his first ball of his new spell. He struck eight boundaries during his 94-ball stay on the crease.
Earlier, Bangladesh were dismissed in their first innings at 305 and took the early wicket of opener Matt Renshaw to complete a satisfying first session on day two of the second and final test.
The visitors were 15-1 at lunch with skipper Steve with 8 and his deputy David Warner with 2 on the crease.
Bangladesh skipper Mushfiqur Rahim took an eye-catching diving catch to dismiss opener Renshaw for 4 off Mustafizur Rahman delivery.
But afterward all three Australian were dropped by the butterfingered Bangladeshi fielders.
Earlier, Nathan Lyon grabbed 7-94, his second best figure by allowing
Bangladesh to add only 52 runs to their overnight total of 253-6.
The off-spinner, who had bagged five wickets on the first day, struck a crucial blow as he dismissed Mushfiqur Rahim with his second delivery of the day 68.
Ashton Agar dismissed the other overnight batsman Nasir Hossain for 45 with Matthew Wade took the fine catch.
Warner then ran out Mehedi Hasan before Lyon accounted Taijul Islam to finish his seventh wicket haul.