Goals from Alanna Kennedy and Sam Kerr in Perth guided the Australians into the last four while also securing a berth at the 2027 finals in Brazil, with World Cup tickets available for the top six finishers at the continental championship.
The Australians, chasing their first Asian title since 2010, will face either defending champions China or Taiwan in the semi-finals on Tuesday with the final to be played in Sydney next Saturday.
"Games like this do something special, they make you believe," said Montemurro.
"I think that's what this team has needed from day one – to believe they are a world-class side, that they can compete at the top level, and to adapt accordingly.
"Now the players believe they can keep improving, getting better and better and that's the most important thing for me. Of course, the FIFA World Cup is important, but so is building that belief."
The Australians have only won the Women's Asian Cup once since joining the Asian Football Confederation in 2006 and missed out on the semi-finals in the most recent edition in 2022.
Chelsea forward Kerr, who doubled her side's lead in the 47th minute, said qualification for the World Cup had been a key objective.
"For us as a footballing team, it's the pinnacle," said Kerr.
"So to put our team there is an amazing feeling."
"Brazil is a footballing nation. What an amazing World Cup to go to. It will be incredible. I hope I'm there. Just the fact that we all get the opportunity to be on the biggest stage is incredible."