The pair smashed the ball to all parts as they scored at more than two-runs-per-ball but after Head was caught on the boundary for a 29-ball 56 wickets tumbled and the rate slowed.
From 0-104 Australia slumped to 4-130 with Marsh among them for a 27-ball 54.
It could have been worse. Josh Inglis, who was the next best score with 27, should have been stumped first ball.
His eventual departure prompted another clatter of wickets, the last five going down for seven runs in 12 balls.
Nevertheless, Head declared: "I think we'd have taken 181 at the start," adding the wicket became harder to bat on as the ball grew soft.
Marsh, playing his first match of the tournament after suffering a testicular injury, highlighted the top order verve Australia have been missing with eight fours and a six.
Head had made 50 runs combined in his past four innings, but he reached that landmark in 27 balls with a brutal display of hitting, posting seven fours and three sixes.
With the pair rampant Australia, who had been put in to bat, were 0-70 at the end of the six-over power play with Marsh hitting the final five balls, bowled by the dangerous Maheesh Theekshana, to the boundary.
Co-hosts Sri Lanka had also suffered a major blow when seamer Matheesha Pathirana suffered a calf injury four balls into his opening over and was unable to continue.
But in mid-innings the spinners changed the game.
Head's exit brought in Green but he was quickly stumped. With scores of 21, 0 and 3 in the competition he is under pressure for his place given the arrival of Steve Smith and the good form of Matt Renshaw, who made way for Marsh despite being top scorer in the defeat to Zimbabwe with a 44-ball 65.
That shock loss had left Australia needing to win this match, or rely on Zimbabwe losing to both Ireland and Sri Lanka.
Marsh was then lbw on review, Tim David (six) caught in the deep and Glenn Maxwell (22), having been dropped on 18 by Pathum Nissanka, a skier, brilliantly caught by the same fielder reverse sweeping Dushan Hemantha.
There was no rousing finish as Marcus Stoinis (4) perished cheaply as did Cooper Connolly (3) and Xavier Bartlett (0) who had replaced Matt Kuhnemann and Ben Dwarshuis, in part to strengthen the batting, albeit they are primarily bowlers.
However, 181 was still more than the record chase on this ground, set more than a decade ago.
