The result was the first Melbourne Cup win for both jockey and horse trainer.
Hot favourite Incentivise led in the straight, but was passed by the Chris Waller-trained horse, ridden by James McDonald, which won the $4.4 million first prize, with Spanish Mission in third.
The win was Verry Elleegant's 10th Group One win, including last year's Caulfield Cup. The mare had come third in last week's Cox Plate.
An emotional McDonald, who won his first Melbourne Cup, praised his mount for her ability.