A victory for Denmark would have moved them to within touching distance of the knockout stage, but Jedinak's 38th-minute spot kick following a VAR review saw the points shared.
Denmark have moved to the top of the section on four points, with Australia still third on a single point. France, however, will rise to the summit - securing their spot in the knockout round in the process - if they beat Peru later this afternoon.
Australia boss Bert van Marwijk selected the same XI that started against France last time out, while Denmark's team showed just one change from their 1-0 win over Peru - Lasse Schone replacing the injured William Kvist.
Denmark were ahead in the seventh minute, however, when Tottenham Hotspur attacker Christian Eriksen fired a powerful effort past Australia goalkeeper Mathew Ryan following an excellent flick from Nicolai Jorgensen.
Sisto tested Ryan with a long-range attempt in the 22nd minute as Denmark looked for a second, before Jorgensen somehow headed a Henrik Dalsgaard cross wide of the post from close range.
Robbie Kruse then had a strike blocked inside the Denmark box following smart work from Leckie in the 30th minute, but Australia were level from the penalty spot in the 38th minute.
The referee had initially missed a Poulsen handball inside the Denmark box, but VAR called for a review, and the decision was eventually given. Jedinak scored a spot kick against France, and the Aston Villa midfielder also made no mistake in this match as he sent the ball past Kasper Schmeichel.
Denmark came close to regaining the lead late in the first period when Eriksen delivered a wonderful free kick into the Australian box, but Ryan managed to gather following a period of panic.
Sisto had a super chance to score a second for Denmark in the 51st minute following another smart flick from Jorgensen, but the attacker fired the ball wide of the post.
Mooy fired a powerful attempt wide of the Denmark post 20 minutes from time, before Rogic forced a smart save from Schmeichel during an open period of the match.
Leckie continued to impress for Australia in a wide position, and the number seven forced Schmeichel to make another save in the 75th minute.
Australia had two more chances in the latter stages, but Arzani and Leckie were both denied by the Denmark goalkeeper once again as the points were shared on the afternoon.
Denmark will end their Group C campaign against France on June 26, while Australia - who can still qualify - finish against Peru on the same day.
DENMARK (4-2-3-1): Schmeichel; Dalsgaard, Kjaer, Christensen, Larsen; Delaney, Schone; Poulsen (Braithwaite 59'), Eriksen, Sisto; N.Jorgensen (Cornelius 68')
AUSTRALIA (4-3-3): Ryan; Risdon, Milligan, Sainsbury, Behich; Jedinak, Rogic (Irvine 82'), Mooy; Kruse (Arzani 68'), Nabbout (Juric 75'), Leckie