After a goalless first half in which Denmark looked lively and had more possession, Australia scored on the counter in the 60th minute when Leckie got past the Danish defence and twisted into space before slotting the ball home.
And while the Socceroos' will embrace the now very familiar underdog role in that game, striker Mitch Duke, high on the adrenaline of a win over the Danes, said that belief in the group was high.
"Mate, bring on whoever. I feel like we could take on anyone right now," he laughed. That's the belief we have in the group. We go out with that mentality that we went [out with] tonight, I think we could go up against anyone and get a result."
The Australians have qualified for the knockout rounds for only the second time, having also done so 16 years ago, when they lost 1-0 to Italy in the round of 16.
"I'm proud, exhausted, everything really. It's hard to describe the emotions right now," Leckie told Australian broadcaster SBS.
"We always knew we could do it as a group. We had our doubters but our spirit, our belief, our work ethic and how close we are as a group shows on the pitch.
"The last 15, 20 minutes we battled until the end. It didn't matter what they threw at us, we weren't conceding. We'll make the most of it tonight, but then it's all about recovery."
Denmark coach Kasper Hjulmand said his side had been "too emotional" with "too little quality" against Australia.
"We haven't played with the tempo and the rhythm in our own game," Hjulmand told a news conference.
"I think we started pretty well tonight, with good positions. And then you see the structures just go out of the match.
"It's too emotional and too little quality, and it's the only thing we shouldn't do against Australia in a match like this, go in with big emotions and lots of fight -- we have to play with quality."
Denmark created chances in the first half and could have taken an early lead but Jesper Lindstrom's shot from close range was blocked before Australia goalkeeper Mat Ryan parried away an attempt from Mathias Jensen.
Australia's defence were guilty of gifting space to Joakim Maehle on the left in the 19th minute as the defender drilled the ball into the box, but Ryan once again came to Australia's rescue, kicking the ball away.
They finally broke the deadlock at the hour mark as Leckie timed his run perfectly and sent the ball through Maehle's legs before beating Schmeichel.
Denmark thought they had been handed a lifeline 10 minutes later when the referee awarded a penalty for a foul on Kasper Dolberg, but it was quickly overturned after the flag was raised for offside.
"We've been working on this for four-and-a-half years, and I could see in their eyes they were ready tonight," Arnold said.
"No celebrations tonight! That's why we won after a great win against Tunisia -- no celebrations, no emotion, sleep and no social media."