Australia, who are playing in their fifth World Cup finals, need a positive result to maintain realistic hopes of qualifying for the last-16 for the second time in their history.
Australia have only reached the second phase of a World Cup once, in 2006 when a late Harry Kewell goal earned them a point in their final group game, putting them ahead of Croatia.
Australia began the second half in bright style but were nearly behind again after 51 minutes when neat build-up play resulted in a chance for Sisto, whose snap-shot went wide.
"We have to give the same performance against France, with a lot of discipline, but improve in the things which can make a difference".
Andrew Nabbout's shoulder injury, which will sideline him for the rest of the World Cup, did not quell Australia's momentum, even though some questioned van Marwijk's decision to replace him with Tomi Juric and not Tim Cahill.
Rogic was heavily involved in Australia's push for a victor in the second half, and tested Leicester City man Schmeichel but could not find the elusive goal. However, their chances of qualification now look slim.
Better finishing - and just a third World Cup win in the nation's history - will be required if the Socceroos are to beat Peru. Is it time for Cahill?
Two-time champion Argentina risks an embarrassing first-round exit after second-half goals by Croatia's Ante Rebic, captain Luka Modric and Ivan Rakitic.
Peru missed a VAR-awarded penalty against the Danes in their first game, while Australia will feel justice has been served after they conceded a debatable penalty following video replays in the loss to France.
Victory also secured France's spot in the tournament's next stage.