Australia have reached the World Cup knockout stage for first time in 16 years after beating Denmark 1-0 on Wednesday.
The Socceroos and the Danes were both in danger of crashing out of the tournament due to Tunisia taking the lead against France in the other Group D fixture.
But Leckie had other ideas and delivered the knockout blow with a superb solo effort in the 60th minute to send Australia into the last 16 for the first time since 2006 in Germany – and only the second time in their history.
They finished in second place in Group D on six points, behind world champions France only on goal difference after the world champions fell to a shock 1-0 defeat.
“I'm so proud of the effort by the boys,” said Australia manager Graham Arnold, whose team had lost 4-1 to France in their opening game. “There was a short turnaround but their effort was incredible.
“A lot of belief and hard work. These boys come in with a great mindset. We've been working on this for the last four/four and a half years about the belief, the energy and the focus. I could see in their eyes, they were ready tonight.
“No celebrations! That's why we won after a great win against Tunisia, no celebrations, no emotion, sleep and no social media.”
Defeat at Al Janoub Stadium capped a miserable campaign for the Danes who finished bottom of the group after taking one point from three games.
The scenes of Australian jubilation at the end provided a stark contrast to what had been a strangely quiet atmosphere for much of the match in Qatar.
Euro 2020 semi-finalists Denmark, who had to win to stand any chance of going through, were on top in the early stages.
Australian defender Milos Degenek, the only change from the team that beat Tunisia 1-0, denied an almost certain Denmark goal with a crucial block.
Denmark's Mathias Jensen, the Brentford midfielder, shot powerfully at goal and was denied by goalkeeper Mathew Ryan in the 11th minute when he probably should have passed.
Socceroos captain Ryan was in the thick of it again soon after, frantically hacking the ball away with his feet after an incisive run down the left by the dangerous Joakim Maehle.
Riley McGree stung the palms of Denmark goalkeeper Kasper Schmeichel on a rare Australian counterattack.
Australia were just about on top when a sterile first-half meandered to a goalless conclusion.
Australia and Denmark both made one change at the break and spectators at Al Janoub Stadium would have been hoping it might trigger a bit more action in the second half.
Jackson Irvine scooped over the bar shortly after the restart for Australia and then the shock news filtered through that Tunisia had taken a surprise 1-0 lead over a weakened France team.
Denmark manager Kasper Hjulmand had already decided to make a double substitution, bringing on forward Kasper Dolberg and attacking midfielder Mikkel Damsgaard.
One minute after that, on the hour, Australia took the lead.
Leckie found himself one on one with an exposed Maehle on the left and turned him inside out before pinging the ball into the bottom corner past Schmeichel. Cue pandemonium from the Australian bench.
Denmark thought they had won a penalty in the 70th minute but there was an offside and their World Cup hopes slipped away without much of a fight.