It was a tight, at times nervy affair at Hampden on a night when the life of Bertie Auld was celebrated by fans.
The Lisbon Lion died last week at the age of 83 and both sets of fans took part in a minute’s applause in his memory.
Substitute James Forrest pounced to score the winner after 74 minutes when he lashed Liam Gordon’s attempted clearance into the net to set up a final against either Rangers or Hibs, who play on Sunday.
Auld might have won the European Cup with Celtic but Forrest, 30, is now targeting his 20th major honour with the Parkhead club in next month’s final.
“It’s always good when people tell you about what you’ve done in the past but I am still playing in the now,” said Forrest. “So I want to keep adding to it.”
Postecoglou is also desperate to lift the trophy – but for different reasons. He wants to kick-start his career at the club with a maiden win.
Despite only arriving this summer he is painfully aware that last season was the first time Celtic had failed to win a major honour since 2009-10. He is impatient to bring silverware to the club in his first season.
“I’m determined to come back and win the trophy,” he said. “It’s not about me personally.
“I understood when I took this role that it’s the measure. Yes, I have a vision of how I want to play football and build a team.
“But ultimately I knew the measure would be how quickly I can bring success to Celtic.
“I’m not going to get two or three years to do that. I came here to try and get this club back to where it should be. Now, I have an opportunity to do that in the final and that has to be our aim.”
Postecoglou dedicated the win to the memory of Auld. The players all wore the No 10 on their shorts and the fans unveiled a huge banner depicting the legend in the 67th minute.
“The tribute to Bertie is an important part of what this club is about,” he said. “The players wore the 10 on their shorts and I said to them after the game, we’re celebrating an immortal of this football club and the Scottish game.
“But we also have to understand there’s some sadness there for the people who are closest to him and his family.
“I’m hoping after that 90 minutes maybe they had a bit of a smile on their face and felt better for a moment. We thought about the great man and hopefully he was looking on from above. These things are important.”
"If you’d asked me beforehand if we could limit Celtic to three or four chances I’d have snapped your hand off," said Davidson.
"The boys worked extremely hard, we tried to work off our shape and limit them. They have defended their trophy with a lot of pride and it’s credit to them that we are disappointed at losing a semi-final to Celtic."