The semi-professional side from NPL Victoria had knocked off Western Sydney 3-0 in the round of 16, following it up with a 4-0 thumping of Wellington Phoenix in the quarter-finals.
Last season's Premiers Plate winners Auckland, led by master coach Steve Corica, was expected to end Heidelberg's fairytale on Saturday night.
But spurred on by their vocal home fans, Heidelberg took the lead in the 75th minute via Bul Juach, before Asahi Yokokawa sealed the deal in the 84th minute.
"When the first one went in, I thought I could cry," Heidelberg captain Ben Collins told Paramount.
"And when the second one went in - the emotions through the body were ... I don't know what to say.
"We had to suffer a little bit today. It was a graft. It wasn't our prettiest game, but the boys took their chances up front."
There were wild celebrations upon the final whistle, with Heidelberg having the chance to create history when they take on either Avondale FC or the Newcastle Jets in the Australia Cup final.
"Honestly I'm speechless. I'm so proud of the boys, so proud of the staff," defensive midfielder Anthony Lesiotis said.
"We worked so hard for this moment, and we've believed the whole way through we can beat anyone.
"We played so brilliantly today and the past few weeks. They're a fantastic opposition and we know the quality they hold.
"We needed a near-perfect performance and I think that's what we did.
"Defensively we were so strong, everyone put their bodies on the line."
Heidelberg took the lead when Auckland goalkeeper Michael Woud charged out of the box to cut off a long pass but failed to make connection.
Juach took full advantage, bumping off his opponent while dribbling the ball, before putting the finish away.
It was party time nine minutes later when Yokokawa threaded the ball through Woud's legs from a tight angle, with the goal sending the players and the crowd into raptures.
