Kulasekara tormented the right-handers with his in-swinging deliveries while Lasith Malinga (3-14) polished off the tail as Australia collapsed in 26.4 overs with only Mitchell Starc (22 not out) and Xavier Doherty (15) managing double digits.
Number nine Starc took a couple of blows on his helmet but hung on to take Australia past their previous lowest total of 70 that came on two occasions, against England in Birmingham in 1977 and New Zealand at Adelaide in 1986.
Angelo Mathews drew first blood with the seventh delivery when he removed opener David Warner and Australia captain Michael Clarke was soon left to rue his decision to bat first at Gabba as the batting order came unstuck.
Kulasekara was on a hat-trick after removing David Hussey and George Bailey off successive deliveries but Matthew Wade denied him the personal milestone.
That was hardly solace for the hosts as the 30-year-old bowler returned to peg back Clarke's middle stump and push one through Moises Henriques's gate for his first five-wicket haul.
Malinga removed Mitchell Johnson, Wade and Clint McKay while Shaminda Eranga, replacing Ajantha Mendis, dismissed Doherty to end the Australian innings.
The five-match series is level 1-1. (Reporting by Amlan Chakraborty in New Delhi; Editing by Alastair Himmer)
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