Australia held strong against a star-studded American team who could not break down the Matildas defence, before playing it safe in the final stages to secure their place in the knockout round.
The scoreless draw secured third place in Group G for the Aussies, with coach Tony Gustavsson putting faith in other results to not only book a quarterfinal place but also avoid an early matchup against the Dutch.
It proved to be the perfect plan as the Netherlands thrashed China 8-2 to top their group and set up a quarterfinal against the USA, while Australia will take on Group E winner Great Britain.
Previously unbeaten in 44 games before that Sweden loss, USA struggled to make the most of their firepower up front.
Alex Morgan's disallowed goal for offside was the closest they came to doing so.
Mary Fowler had the best of the Matildas' chances when she hit the crossbar with a powerful header midway through the first half.
Australia looked the better of the two sides in the opening 45 minutes as the Americans tried to settle into the contest.
Tameka Yallop had a brilliant effort on goal denied by the keeper and Sam Kerr created headaches for the opposition defence whenever she was on the ball.
The second half was a much slower affair with both side's seemingly happy to hold on for a draw, with only a few chances created by either side.
While it wasn't pretty, The Matildas did enough to keep their Olympic tournament hopes alive.
RAMPANT DUTCH AWAIT USA
Sweden were already assured of a place in the last eight ahead of their clash with New Zealand and saw the job through with a 2-0 win at Miyagi Stadium to finish ahead of USA.
Anna Anvegard and Madelen Janogy were on target for Sweden before half-time and they saw out a straightforward win that condemned New Zealand to a group-stage exit.
It means USA will now take on the Netherlands in the next round in what is a repeat of the 2019 Women's World Cup final. The Netherlands lost that match, but they enter this latest showdown in superb form after thrashing China 8-2 in Yokohama.
Lineth Beerensteyn, Lieke Martens and Vivianne Miedema all scored twice in the one-sided affair, while Shanice van de Sanden and Victoria Pelova were also on target.
The Netherlands' tally of 21 goals from three games is already the most scored by a team in a single women's football Olympics event, surpassing the USA's 16 from London 2012.
HOSTS JAPAN SCRAPE THROUGH
Japan did all that they could in the final round of group games by beating Chile 1-0 through a Mina Tanaka goal 13 minutes from time.
That win took the tournament hosts to four points from three games, enough to send them through as one of the best third-placed sides, along with Australia.
Already through to the quarter-finals, Great Britain snatched top spot with a late 1-1 draw against second-placed Canada in Tuesday's other Group E match.
Caroline Weir's long-range free-kick with 84 minutes played took a heavy deflection and cancelled out Adriana Leon's opener.
Brazil also booked their spot in the knockout stages thanks to Andressa's first-half free-kick in their 1-0 win against the tournament's lowest-ranked side in Zambia, who lost Lushomo Mweemba to an early red card.
The Selecao meet Canada in the quarters, while Australia await Great Britain.