Gonzalez's Real team-mate Athenea del Castillo converted a penalty to seal the win, despite Spain missing 15 top players who are embroiled in a row with coach Jorge Vilda.
Spain end the four-team Cup of Nations - a dress rehearsal for the World Cup in Australia and New Zealand in July-August - with two wins from three.
The Euro 2022 quarter-finalists beat Jamaica 3-0 but lost 3-2 to hosts Australia.
The unbeaten Australians round out the tournament against Jamaica later Wednesday needing a draw to win the trophy.
Spain applied all the early pressure in the rain at Newcastle, north of Sydney, with the breakthrough coming on 28 minutes after a neat series of passes ended with Gonzalez tapping in from close range.
The experienced striker doubled the lead 10 minutes later with a header, before Del Castillo made it 3-0 from the penalty spot with six minutes left.
Spain have two more international windows left to tune up for the World Cup and for the 15 players, including a large Barcelona cohort, to decide whether they want to play under Vilda again.
None have featured since September when they made themselves unavailable for selection, reportedly unhappy at the locker-room atmosphere and his training methods.
The Spanish FA backed the coach.
