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.
But Jussuf Poulsen's handball after a video review set up Jedinak's opportunity in the 38th minute.
A draw would have put them in the driving seat for the round-of-16 qualification but a late own goal from Aziz Behich dashed those hopes as France ran away atop of Group-C.
With a loss to France in the opener, a defeat Thursday would have made it almost impossible for the Socceroos to advance to the next stage.
MASSIMO Luongo and Australia's hopes of qualifying for the second round of the World Cup remain in the balance following an entertaining 1-1 draw with Denmark. Australia definitely had the Danes' measure in the second-half, with better positioning and more attacking play.
"When you are at this level and create so many chances against Denmark I must be happy with the number of chances, the only thing we have to do is put the ball in the goal".
"Two matches in a row against us".
Aaron Mooy went close from distance for Australia before Denmark's Pione Sisto was left holding his head after a curling shot from outside the area flashed just wide. Instead, Denmark fell victim to the system, which has worked well so far in the World Cup but isn't ideal. Australia added some firepower in the 68th, bringing on 19-year-old Daniel Arzani as both teams scrambled for a winning goal.
Denmark will be looking to book their place in the knockout stages of the competition with a victory over Australia.
Eriksen, who plays for Tottenham in England, has scored in 17 of the national team's last 20 matches.
"For me it is important just that we have to beat Peru", Australia coach Bert van Marwijk told reporters.
The Danes said before the game that they were keen on getting back to the free-flowing football that has characterised the team.