Australia reached their first Olympic semi-finals after a thrilling 4-3 victory over Team GB after the game ended 2-2 in normal time.
But Australia proved resilient and defended well and took their chances as their opponents created opportunities but defensive frailties were to be their undoing.
Team GB hit the woodwork three times in the opening half hour but it was Australia who scored first as Alanna Kennedy was allowed a free header from a corner.
The Matildas began the second half strongly but again it was the team who were struggling who scored. A header from White levelled. The Man City player then fired GB into the lead after the Aussies failed to clear their lines.
And GB looked to be heading into the semis but their defending ever deeper cost them as with a minute remaining Sam Kerr was given too much space to fire home and send the game into extra time.
Team GB had the perfect start when awarded a penalty for a foul on Nikita Parris but Caroline Weir saw her weak penalty easily saved by Teagan Micah. The keeper then immediately made two more saves in quick succession to keep her team in contention.
The Matildas then broke quickly and regained the lead as their youngest player Mary Fowler saw her shot from distance deflect off Lucy Bronze and into the top corner.
The game looked over for Team GB as within a minute of the restart of the second period of extra time Sam Kerr rose highest to give the Matildas a two goal cushion via the underside of the cross bar.
Back came Team GB and gave themselves hope when White headed her third goal with five minutes remaining but despite constant pressure Australia's defence held firm and a place in the semis on Monday.
Team GB: 3 (White 57, 66, 115)
Australia: 4 (Kennedy 35, Kerr 89, 106, Fowler 103)
Venue: Kashima Stadium, Kashima
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