The New Zealand mare - ridden by James McDonald - chased down the short-priced favourite in the home straight to win by four lengths.
It is the first Melbourne Cup victory for trainer Chris Waller.
"I love her to bits. She's been so good to me," McDonald told local network Channel 10 after the race.
"They can safely say she's a champion now.
"I never thought I would ever win one, you know. I always dreamed of winning one, but, it's so hard to win."
Last year's winner, Twilight Payment, trained in Ireland by Joseph O'Brien, finished 11th after heading the weights.
The Melbourne Cup, known as "the race that stops a nation", is worth A$7.75m (£4.25m; $5.8m).
It usually attracts a crowd of about 100,000 but only 10,000 fully vaccinated racegoers were present this year because of Covid-19 restrictions.
Immediate reports suggested all runners had got through the race unscathed.
Stricter checks on overseas runners were introduced after six equine deaths associated with the race since 2013.
The 2019 Derby winner Anthony Van Dyck was euthanised after suffering a broken leg in last year's race.
Spanish Mission had been cleared by vets to run for Andrew Balding after being treated for swelling in one of his legs.