Bangladesh needs to defend 127 runs to win the series with two matches to spare in the five-match T20 internationals against Australia on Friday.
Earlier, after winning the toss and electing to bat first, the hosts put up a modest total of 127 for the loss of nine wickets.
Skipper Mahmudullah top scored for the tigers with 52, while Shakib scored a quickfire 26(17) to help Bangladesh reach the modest score on a bowling-friendly pitch.
Both Shohan(11) and in-form Afif(19) was run out courtesy of some brilliant fielding by the visitors.
Debutant Ellis clinched a hat-trick in the last 3 balls of the innings. Hazlewood and Zampa took 2 wickets each for the Aussies.