On a slow track, Yuvraj initially struggled before blasting four sixes and five boundaries in a 43-ball knock. It was also his eighth T20 International half-century in 38 matches.
Skipper Mahendra Singh Dhoni played the role of second fiddle to perfection, contributing 24 in an 84-run partnership for the fifth wicket.
Dhoni lost the first toss in the tournament and as Ravichandran Ashwin had said yesterday, were forced "swim a tsunami" considering the adverse conditions for batting first on a slow Sher-e-Bangla track.
Australia opened their bowling with Brad Hodge and he got success removing the in-form Rohit Sharma (6) with a slider which the player tried to drive but got a thickish outside edge which went to James Muirhead standing at backward point.
Virat Kohli started with a slog sweep off Glenn Maxwell that went for a six and followed it by guiding Mitchell Starc to the third man boundary. But it didn't last long enough as he tried to hoist leggie Muirhead over long-off but failed to clear Cameron White stationed for that catch. Kohli's 23 came off 22 deliveries with two fours and a six.