At the other end, Mathew Leckie rose above the Danish defence to head a corner over the bar but Denmark countered and Nicolai Jorgensen's elegant ball control and lay-off afforded Eriksen the chance to hit the cleanest of half-volleys over Mat Ryan and into the top of the net.
Eriksen's seventh-minute opener was fully deserved by the fast-starting Danes and the quality of his half-volley finish was excellent in a tournament that has produced some wonderful goals.
That was the last meaningful action of the contest, with both nations having to settle for a share of the spoils which maintains their respective hopes of making it out of Group C and into the knockout stages.
Eriksen opens the scoring against the Socceroos.
Denmark closes against France, while Australia faces Peru on Tuesday at 10 a.m. ET.
"The goalkeeper will do what he has to, to make him feel bigger than he is", said Jedinak.More news: Trump to sign executive order to end family separations at the border
Australia again took a defensive stand against Denmark, which was back at the World Cup after missing out on the tournament in Brazil. Poulsen, who plays for German club RB Leipzig, scored the lone goal.
Neither side could create a meaningful goalscoring opportunity as the half wore on, Aaron Mooy firing wide with 20 minutes remaining before Tom Rogic forced a low save from Schmeichel.
After the pleas from Denmark's players to the referee went unheard, Schmeichel had a few words with Jedinak to rattle him.
It was Eriksen's 13th goal in his last 15 appearances for his country and underlined the pivotal importance of the Tottenham Hotspur playmaker to the otherwise workmanlike Danes.
"You still have to stay focused in getting good contact and maintain that focus", said Jedinak, who plays for Aston Villa.
Australia battled back impressively in Samara after Christian Eriksen's sweetly-struck half volley, before Denmark faded badly in the second half.
The Socceroos were quickly into their stride after the restart, only for Pione Sisto to curl just wide of Ryan's goal.