Denmark's forward Martin Braithwaite, left, vies with Australia's midfielder Jackson Irvine during the Russian Federation 2018 World Cup Group C football match at the Samara Arena in Samara on Thursday.
There will be questions over the awarding of the penalty, with VAR intervening to spot a marginal handball from an Australia corner.
Bert van Marwijk's team lacked the compactness and composure they showed in the early stages of their game against France on Sunday and it was hardly a surprise when the Scandinavians took the lead in the 7th minute through their star player.
Jedinak made no mistake from the spot, as he ignored goalkeeper Kasper Schmeichel's attempts to distract him and sent the Leicester City man the wrong way.
Denmark's players celebrate after Christian Eriksen's goal to open the scoring in Samara.
With a loss to France in the opener, a defeat on Thursday (Friday NZT) would have made it almost impossible for the Socceroos to advance to the next stage.
Jedinak, however, got Australia back into the game with his second penalty in Russian Federation, awarded following the intervention of the VAR, and the draw kept the Socceroos just about alive in the tournament. But the score didn't reflect the Socceroos' gritty defensive performance.
The Danes won 1-0 in their last match against Peru, thanks to a Yussuf Poulsen goal.
The goal seemed to galvanise the belief among the Australian players, who started the second half well on top.
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Australia was also making a fifth trip to the World Cup.
Pione Sisto almost gave the Danes the advantage just after the halftime break, but his shot went to the right of the goal.
Denmark should have doubled their advantage when Jorgensen flashed a header wide at the near post as Australia looked ragged at the back and toothless up front.
Denmark will be without midfielder William Kvist, who sustained suspected fractured ribs in the first half against Peru. He was replaced in the starting lineup against Australia by Lasse Schone.
Last time the Socceroos faced Denmark they were trounced 4-1 in Oslo. He has 79 appearances for the national team and 23 goals.