Blake Govers scored a hat-trick for the hosts, including a last-minute winner from a penalty corner.
Two Ashley Jackson goals put Britain 2-0 ahead, but Govers scored twice and Matthew Dawson once to put Australia in front, before Sam Ward made it 3-3.
Saturday's opening match ended 2-2, so the hosts hold a 1-0 series lead going into Tuesday's final Test in Perth.
It was the second time in two days that GB had squandered a winning position against the world's number-one ranked team.
"Our performance today was littered with inconsistency," said GB head coach Bobby Crutchley.
"We had some decent spells, but suffered too many turnovers in possession. We will be looking for improvement in the third Test."

Peter Metcalf was involved in defending the force against unlawful arrest claims after the 1984 Orgreave clash.
He also played a key role in reviewing statements after Hillsborough.
Deputy Chief Constable Peter Hayes and Assistant Chief Constable Walter Jackson are connected to both cases.
The officers, who were involved in a review of the evidence after Orgreave and have links to Hillsborough, have both denied any wrongdoing.
Mr Metcalf did not wish to comment on Orgreave when approached by the BBC.
About 10,000 strikers and 5,000 police officers clashed at Orgreave coking plant in June 1984.
Mr Hayes ordered a review of the way evidence had been gathered about Orgreave and was later involved in co-ordinating the force's evidence after the disaster at the Sheffield stadium.
Mr Jackson was given the job of reviewing the Orgreave evidence and was at Hillsborough to watch the FA Cup semi-final after signing off the policing plan.
The parallels between Hillsborough and Orgreave have been drawn before. Now evidence is starting to emerge showing the actual links, the names of people involved in the aftermath of both.
There have been claims the way South Yorkshire Police conducted themselves after 'The Battle of Orgreave' fed into their response to the Hillsborough disaster.
There have been growing calls for some form of investigation to fully understand what happened during the miners' strike and how that may have shown a culture within the South Yorkshire force that endured long after.
But it should also be remembered these are very different incidents. Nobody died at Orgreave. Although miners were put on trial, the cases collapsed so there was no miscarriage of justice. That said, the miners have always carried a sense of injustice about what happened. Their calls for an inquiry now have the backing of some of the Hillsborough families. It's up to the home secretary to decide what happens next.
Mr Metcalf wrote a note saying he had been told some of the police statements did not match the video evidence at Orgreave.
His note also records Mr Metcalfe as saying that he had been told that senior officers were reluctant to provide anything that might undermine the case.
Last year, the Independent Police Complaints Commission (IPCC) said it had identified possible cases of attempting to pervert the course of justice in relation to Orgreave.
However, the police watchdog decided an investigation was not in the public interest.
Former miners' union president Arthur Scargill has called for an inquiry into the Battle of Orgreave disorder.
More than 120 officers and pickets were injured and 93 people were arrested following clashes at the coking plant.
Campaigners have called on Dave Jones, the interim chief constable of South Yorkshire Police, to open up the force's archives on Orgreave.
The Orgreave Truth and Justice Campaign said it wanted Mr Jones to intervene in its legal bid to push Home Secretary Theresa May to hold a public inquiry.
Mr Jones said he would "welcome an appropriate independent assessment of Orgreave".
"The Hillsborough inquests have brought into sharp focus the need to understand and confront the past and give people the opportunity to explore the circumstances of such significant events," he said.
In the aftermath of the Hillsborough disaster, police accounts of what happened were amended, in some cases to remove criticism of senior officers.
In contrast to their professional training, police officers at Hillsborough were told not to record the day's events in their pocket books but to set down their "recollections". In an "unprecedented process of review and alteration", they were then edited by the force's lawyers before submission to the official inquiry.
Great Britain surrendered a two-goal lead to lose 4-3 to Australia in a dramatic second Test in Narrogin.
[NEXT_CONCEPT]
Senior officers and a solicitor who were involved in the South Yorkshire Police response to Hillsborough and the so-called Battle of Orgreave can be named for the first time.