Australia make 178-8 against Windies
Australia batsman Brad Hodge plays a shot during the ICC World Twenty20 tournament match between Australia and West Indies at the Sher-e-Bangla stadium in Dhaka on March 28, 2014 - by Punit Paranjpe
Six of the eight wickets fell to spinners after Australia elected to take first strike, with Samuel Badree, Marlon Samuels and Sunil Narine claiming two wickets each.
Glenn Maxwell hit 45 off 22 balls at the top of the order, while Brad Hodge chipped in with a 26-ball 35 during a sixth-wicket stand of 52 with James Faulkner.
Both teams, who have lost a game each, need a win to remain in serious contention for the semi-finals.
Australia were beaten by Pakistan in their only game so far, while defending champions West Indies lost to India before defeating hosts Bangladesh.
A second loss for either team will almost certainly hasten an early exit.
Openers David Warner and Aaron Finch plundered 33 runs off the first 22 balls when the West Indies hit back with three wickets in the next two overs.
Finch and Warner were bowled trying to hit against the spin, while Shane Watson was stumped on second attempt by Denesh Ramdin in Narine's first over.
Maxwell propelled the innings with a stunning knock that contained three sixes and five boundaries before he was fifth out in the 12th over with the total at 100.