City's summer signing added two goals from Caitlin Foord and one from Sam Kerr to complete a comprehensive defeat of the side ranked second best in the world in front of 22,065 fans.
Wearing the No.11, Fowler came off the bench in the second half while City team-mate Hayley Raso started for the home side.
The result is the Matildas' biggest ever-win against a top-5 nation.
Chelsea's Kerr scrambled the first home in the first half before a Foord curling effort made it two just after the break.
Then it was Fowler's turn to shine as Australia went from back to front quickly and our 19-year-old raced forward to join the attack.
Her left-footed effort took a deflection that wrong footed Swedish goalkeeper Zecira Musovic and found its way in.
Foord poked home her second and Australia's fourth a few moments later to complete the scoring on a memorable night for the Matildas.
Khiara Keating is also in action for England Under-19s at the Algarve Cup, where she began with a 2-1 win over Norway on Wednesday.