When Doherty leg-glanced his first ball to the boundary, Australia passed the lowest total by a recognised Test nation - 43 endured in South Africa by both Pakistan (1993) and Sri Lanka (2012).
The spinner's last boundary ensured they crept beyond 70 - which Australia made in 1977 in England and also in 1986 against New Zealand in Adelaide.
It looked to be a superb Brisbane one-day pitch and Michael Clarke had no hesitation in batting first on winning the toss.
While it was Angelo Mathews who struck first by having a returning David Warner caught at mid-off, Kulasekara did the real damage, ripping through the bamboozled top order with a mixture of brilliant swing and seam bowling.
He already had Phil Hughes caught at second slip before dismissing David Hussey and George Bailey off successive inswingers in his fourth over to be on a hat-trick.
Matthew Wade survived but it wasn't long before Kulasekara clean bowled both Clarke and Moises Henriques through the gate with the two best deliveries of the day to have Australia 6-30.
Malinga then chipped in by dismissing Mitchell Johnson, Wade and Clint McKay in quick succession.
Starc wore two bouncers on his helmet but both he and Doherty showed more ticker than their top-order teammates.