The five-year-old gelding pulled clear in the final stretch on a soft track to outpace Goodie Two Shoes and Middle Earth in the energy-sapping 3,200-metre handicap at Flemington.
Last month, Melham became the first woman to win the Caulfield Cup in its 149-year history, guiding the Tony and Calvin McEvoy-trained Half Yours to an emphatic victory in the $5 million handicap over 2,400m.
Ten years after Michelle Payne's breakthrough on Prince of Penzance, Melham became only the second woman to win the Melbourne Cup in the two-mile handicap's 165th running, leading runner-up Goodie Two Shoes by three lengths and with Middle Earth crossing third.
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.
First run in 1861, New Zealand's Maree Davey was the first woman jockey to saddle up at the Melbourne Cup 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."
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.
"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, with the sound of popping champagne corks accompanying the thundering of hooves.
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.
"Oh my god. This is what we do it for," said Melham, who raced as Jamie Kah until marrying jockey Ben Melham this year.
"This is why we get up out of bed every morning, at 4 a.m. and work our arses off.
"The last 15 years I've been in this industry, it's tough. It's not all glorious and perfect, as everyone can see.
"I've had an amazing year, amazing year, got married, had some really great days on the track but nothing ever, ever compares to this feeling right now.
"I've just won the Melbourne Cup."
Final finishing order
1st: 14. Half Yours. $8.60, $2.90
2nd: 20. Goodie Two Shoes. $9.20
3rd: 7. Middle Earth. $8.30
4th: 21. River Of Stars
5th: 23. Torranzino
6th: 4. Vauban
7th: 1. Al Riffa
8th: 9. Absurde
9th: 13. Changingoftheguard
10th: 8. Meydaan
11th: 17. Furthur
12th: 3. Arapaho
13th: 10. Flatten The Curve
14th: 12. Smokin’ Romans
15th: 22. Royal Supremacy
16th: 24. Valiant King
17th: 16. Onesmoothoperator
18th: 15. More Felons
19th: 6. Presage Nocturne
20th: 18. Parchment Party
21st: 19. Athabascan
22nd: 11. Land Legend
23rd: 5. Chevalier Rose
24th: 2. Buckaroo