The MCG was stunned into silence from kick-off as Giuliano, wearing the number 10 shirt typically donned by the rested Neymar, pounced on Mark Milligan's slack pass and sent Souza into the penalty area to finish low to Mitchell Langerak's right.
It meant the 31-year-old Souza, only in the starting line-up following an injury to Manchester City's Gabriel Jesus, registered his first goal for his country on his sixth appearance - nearly eight years after he won his first cap.
Thiago Silva and Taison extended the advantage midway through the second half, before Souza rubbed salt into the wounds with his second deep into injury time.
Alex Sandro hit the bar early in the second-half, but it wasn't too long before Brazil's lead was doubled.
The former Tottenham midfielder, now playing for Chinese club Guangzhou Evergrande, was just eight yards out but scooped his shot high over the crossbar.
Brazil bounced back spectacularly from their 1-0 loss to Argentina at the same venue on Friday with captain for the night Liverpool's Philippe Coutinho and Chelsea's David Luiz outstanding for the South Americans.
Highlanders defeat British and Irish Lions 23-22
They built on that momentum, producing a superb scrum in the 74th minute to blast the Lions off the ball and win the penalty . His withdrawal from the tour was announced hours before kick off against Highlanders in Dunedin on Tuesday morning.
Cahill was used off the bench more often than not for Melbourne City last A-League season, a role he's increasingly assumed for the national team under coach Ange Postecoglou.
"I just have to be thankful for making two goals and being able to help the team win".
Australia, who play world champions Germany in Group B at the Confedations Cup in Russian Federation on Monday, entered the stadium with cautious optimism after last week's win over Saudi Arabia reignited hopes of a fourth straight World Cup appearance.
"My end goal is to get to Russian Federation, but when 23 players are selected it starts from 20 to 60 players who have been a part of this long campaign for two and a half years with the boss", Cahill told reporters.
"You've got in the back of your mind the certain levels you need to be at professionally, and the best thing about coming into camp is being on level pegging with every single player, regardless of age", Cahill said.
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