The Australians were in trouble at 67 for five before Cameron White led an extraordinary fightback with an unbeaten 85 off 49 balls which dominated their total of 168 for five.
White and Michael Hussey (39 not out) added 101 runs, a record sixth-wicket partnership in international Twenty20.
White smashed six sixes and six fours in an explosive innings that put pressure on Sri Lanka.
Sri Lanka opener Mahela Jaywardene, the tournament's top scorer, failed for the first time and his team collapsed to 87 all out against the relentless Australian attack.
Mitchell Johnson was the pick of the bowlers, ending with figures of three for 15 from 3.2 overs.
Australia, who top Group F with four points, need only to avoid a heavy defeat by West Indies on Tuesday in St. Lucia to go through to the semi-finals.
