The five-year-old gelding pulled clear in the final stretch on a soft track to outpace Goodie Two Shoes and Middle Earth by 1.5 lengths in the energy-sapping 3,200-metre (two-mile) handicap at Flemington.
"Oh my God, this is what we do it for," said Melham, formerly Kah, who came third last year aboard Okita Soushi and won the Caulfield Cup on the all-Australian Half Yours in her last ride.
Melham is the first woman to win the Caulfield Cup-Melbourne Cup double.
"This is why we get up out of bed every morning at 4am, it's tough, it's not all glorious and perfect as everyone can see sometimes," she said.
"I've had an amazing year," the 29-year-old added. "Got married, had some really great days on the track, but nothing ever, ever compares to this feeling right now."
Her husband Ben Melham was also racing, finishing 14th on Smokin' Romans.
She joined Michelle Payne, who famously steered 100-1 outsider Prince of Penzance to glory in 2015, as the only women to win the race with the pair embracing afterwards.
First run in 1861, New Zealand's Maree Davey was the first woman jockey to saddle up in the race in 1987. A record four women took part last year and three this year.
"Welcome to the club," Payne, who was commentating, told Melham.
"We have so many young girls coming into our industry and to see her win the Caulfield and Melbourne Cup double is just so fitting. She is such a hard worker."
Payne, who had a movie made of her exploits, has been a mentor to Melham and was emotional.
"I've got tears in my eyes, it's the most incredible feeling and for Jamie, who deserves it, it's even better," she said on broadcaster Channel Nine.
The two other women in the saddle, Celine Gaudry and Rachel King, came fifth and 12th respetively on Torranzino and Arapaho.
Trained by father-son duo Tony and Calvin McEvoy, Half Yours was an early favourite but French galloper Presage Nocturne took over at the head of the market 30 minutes before race start at $7.00.
Half Yours was second favourite at $8.00 ahead of Irish raider Al Riffa, who finished seventh, in cool and overcast conditions for the 24-strong field.
Presage Nocturne finished well out of the placings in 19th.
"What a horse. He's continued to raise the bar. I've got no words, what an amazing horse," co-trainer Calvin McEvoy said.
A cultural institution in Australia, the Melbourne Cup has been run on the first Tuesday of November since 1876 and is considered so important it is a public holiday in its host state of Victoria.
Held in front of a bumper crowd, drinking and socialising took priority over racing for many, despite the miserable weather.
Breaking from barrier eight, Half Yours settled in the middle of the pack behind early pacesetter Land Legend.
With 1,000m to go, Land Legend was eight lengths ahead but tired and was slowly reeled in down the home stretch where Half Yours kicked clear.
Mark Zahra, who won two of the three previous Melbourne Cups on Without a Fight and Gold Trip, could not repeat the feat on Al Riffa.
Kerrin McEvoy on Absurde came eighth in his bid for a record-equalling fourth win.