Kulab's massive 142-kilogram baby was born on Friday morning after a 22-month pregnancy, but zoo staff were desperately worried for both mother and offspring in the later stages of labour.
On Thursday night, Kulab was writhing in pain as her son's legs were stuck in the birth canal.
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Had Kulab not been able to give birth within a short time, the baby would have died and surgery would have been needed to save her.
So, the Asian elephant was sent off for a walk in the paddock with her closest companion, Num-Oi.
Soon afterwards, the birth began quickly and was successful, to the relief of the zoo's team who had been working day and night with Kulab.
An elephant reproductive expert, Thomas Hildebrandt, who also oversaw the birth of female Mali at the zoo in January, said Kulab's ordeal came "very close to a very big disaster".
"We discussed things, it was a team decision and we took account of the mental condition of Kulab," Dr Hildebrandt said.
"It was very successful. It was a big team effort and the best player was Kulab."
Zoos Victoria's senior veterinarian, Helen McCracken, said Kulab had recovered well from the birth and was quick to nurture her son, who weighed in at about 30kg-50kg heavier than average elephant babies.
"We were just elated to see, one big push and the baby was delivered very quickly and very, very quickly Kulab and her companion Num-Oi were very interested in the baby and caring for it really, really well," Dr McCracken told reporters as triumphant-sounding elephants trumpeted in the background.
Both Kulab and her baby are being monitored 24 hours a day to make sure the group of elephants integrate well.
Australia is experiencing a baby elephant boom with four born in the past year.
Male Bong Su, who lives in Melbourne, is father to three of the four baby elephants, including Mali and Pathi Harn at Sydney's Taronga Zoo.
A competition is expected to find a name for the new baby and Victorians will meet him when he is ready, Melbourne Zoo director Kevin Tanner said.
