Sent into bat, Sri Lanka rode on Mahela Jayawardene's unbeaten 81-ball 84 to post 253 for eight, leaving the defending champions with a Herculean task of chasing down the target in 29.1 overs to ensure a semifinal berth from group A alongside England.
Adam Voges and Matthew Wade were batting on 10 and nine respectively, at the 15th over mark.
The Lankans held all the aces, but in the unlikely event of Australia winning the game after 29.1 overs, New Zealand will be through.
Phillip Hughes lasted barely 10 balls as he too was shown the door by Kulasekara who bowled a back of length ball that pitched outside off before inducing a thick edge.
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Glenn Maxwell blazed away to 32 off just 20 balls before being cleaned up by pace spearhead Lasith Malinga. Maxwell smashed five fours and a six during his breezy knock.
More trouble was in store for Australia as they lost George Bailey thanks to a fine piece of fielding from Kulasekara whose flat throw from short fine leg caught the skipper well short of the crease.