Catch up on all the action and highlights from Australia v Denmark now on the
Leckie's superb left-footed strike ensures the Socceroos follow the feats of the so-called golden generation in reaching the round of 16.
"It's first time ever an Australian team has won two games of the World Cup in a row," coach Graham Arnold said.
"Maybe we're talking about a new golden generation now because we've been listening and hearing about the golden generation of 2006 who got four points - and now we've got six."
Leckie, arguably Australia's best World Cup performer over his three tournaments, entered football folklore with the match-winner at Al Janoub Stadium on Thursday (AEDT).
The stalwart, played into space by Riley McGree, broke an hour-long deadlock with his own Danish slice - he ran, teased and then turned his marker Joakim Maehle after gathering some 30 metres from goal.
First to his right, then onto his left, Leckie twisted and turned and fired a low left-footer to spark jubilation.
"As the ball was rolling in, I saw it going in, I was so excited and so happy," Leckie said.
"By the celebration, you see how much emotion there was."
Australia will meet the winners of Group C on Sunday (AEDT).
In the other simultaneous game in Australia's group, outsiders Tunisia had scored just three minutes earlier against holders France, who rested almost their entire first-choice side.
The Tunisian goal - they would ultimately win 1-0 - momentarily lifted them to second in the group behind the French, only for Leckie to restore the Socceroos into that prized slot.
Defender Milos Degenek was informed by sideline staff of the Tunisia score and, while the Australians celebrated Leckie's rapid retort, told his teammates.
They didn't believe him.
"The boys thought it was me psyching them up so we won't lose," Degenek said.
"But it was actually me being serious."
Leckie and his captain Mat Ryan, barring injury, will break the Australian record for most World Cup games in the knockout encounter.
Against the Danes, the duo both made their ninth finals appearance, equalling Tim Cahill and Marco Bresciano's record.
"We're an ambitious group," Ryan said.
"Because, while everyone is enjoying the victory, post-match, out on the pitch, the comments are already coming out - we're not done yet.
"We want to keep going, we want to make this chapter as special as can be."
Goalkeeper Ryan was called into action early as the Socceroos, lacking early spark, were forced to repel a series of first-half attacks from the Danes, ranked 10th in the world, some 28 slots higher than Australia.
But the tide turned in the second half after an Arnold revving.
"I'm just so proud of the players," Arnold added.
"The work ethic, the commitment, the fight that they had and the way they played."
