The regulation time of the intense all-European final ended goalless, forcing the penalty shootout.
This was Australia's fifth bronze medal in the history of the tournament. The last time the Kookaburras had to be satisfied with a third-place finish was way back in 1994 in front of their home crowd in Sydney.
Belgium mauled England 6-0 in a one-sided match, but the Dutch survived a late Australian charge to win 4-3 via a shoot-out.
Australia are second only to four-time champions Pakistan, having won the world title thrice before, which includes back-to-back gold medals in the last two editions of the tournament in 2010 and 2014.
Belgium and the Netherlands registered wins over Germany and India with identical margins in the third and fourth semi-final matches on Thursday.
India took the lead but it lasted only three minutes. Then a superior, smarter and more experienced side took control of the match, taking the lead in the last quarter even as India continue to play the catch-up.
India find themselves in a rare position to go beyond the quarter-final stage in Hockey World Cup for the first time since 1975.
India last played in the semi-final of the World Cup way back in 1975 when they went on to lift their maiden title.
Australia will play the winner of Thursday's last quarter-final between India and the Netherlands in the semi-finals on Saturday.
In a lopsided match, Pakistan failed to match their spirited rivals and were found wanting in almost every aspect of the game.
On Monday, England and France won their respective crossover matches against New Zealand and China to enter quarters.
France, the lowest ranked team in the tournament at 20, have already shown the world that rankings hardly have any significance by stunning Olympic champions Argentina 5-3 in the pool stages.
England will face Olympic champions Argentina in the first quarterfinal on Wednesday.
Both the semi-finals and the final are scheduled for December 15 and 16 respectively.
In the crossover, the Netherlands will face Pool C third-place team Canada, while Pakistan will take on Pool C runners-up Belgium.
The Olympic bronze medallist finished their pool engagements with a maximum of nine points from three games. They have previously defeated Pakistan 1-0 and the Netherlands 4-1.
After a cautious start, India scored goals at will to beat Canada 5-1. The win helped India top Pool C and book a direct quarter-final spot.
Despite the defeat, China will have another chance to qualify for the last eight as they have made themselves eligible for the crossover round after finishing third in Pool B.
A farmer sits near his red chillies at a deserted APMC market, during the weekend curfew imposed by the Karnataka government to curb the spread of COVID-19, in Hubballi.PTI Photo
Delhi Chief Minister & AAP National Convenor Arvind Kejriwal being welcomed by women supporters during his door-to-door campaign ahead of the Goa Assembly elections, in Goa.PTI Photo
A health worker collects swab sample of a woman for COVID-19 test, amid concerns over rising Omicron cases, in Gurugram.PTI Photo
Traffic jam on a road at Shalimar Bagh during the weekend curfew imposed by the Delhi government to curb the spread of Covid-19, in New Delhi.PTI Photo/ Shahbaz Khan
The Lajpat Nagar market wears a deserted look during the weekend curfew imposed by the Delhi government to curb the spread of Covid-19, in New Delhi.PTI Photo/ Shahbaz Khan
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