Having got back into the game, Australia seemed imbued with a renewed sense of belief, surging forward whenever they could and roared on by the vast array of green and gold clad fans in the Samara Arena.
The point was enough to take Denmark to the top of Group C on four points, one ahead of France who play Peru at 16:00 BST, while Australia can still advance to the knockout 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.
"They are physical", Van Marwijk told reporters on Wednesday.
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"We're still in with a sniff", said Jedinak after the game.
3 - Australia are the second team in World Cup history to score three consecutive goals from the penalty spot.
Christian Eriksen scored in the opening minutes for Denmark, which has gone unbeaten in 17 straight worldwide matches.
The Danes enjoyed their best period after this but failed to capitalise on their possession and territorial advantage.
Denmark's talisman Christian Eriksen knows his side must rediscover the attacking dynamism of their qualifying campaign if they are to follow up on their opening victory over Peru with a win against Australia in Samara on Thursday.
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However, if he's going they should use that pick to start the rebuild (and Porter would be a good step that direction). I was talking with my Dad when we mentioned the possibility of how Golden State can get better this off season.
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.
They now head to Samara knowing a win over Australia will put them in the driving seat to qualify from Group C.
"We have to give the same performance against France, with a lot of discipline, but improve in the things which can make a difference".
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.
Andrew Nabbout's game ended prematurely when he fell and suffered what looked like a dislocated shoulder, the Urawa Reds front man replaced by Tomi Juric.
Switzerland Boss Vladimir Petkovic 'Proud and Pleased' After Impressive Draw Against Brazil
Eight years ago in South Africa, Switzerland beat eventual champions Spain in their World Cup opener but failed to advance to the knockout rounds.