The 18-year-old student is believed to be the first person in the UK to appear in a competitive horse race while wearing a hijab.
The amateur rider from Peckham, in south London, won the five-and-a-half-furlong charity race aboard Charlie Fellowes-trained 25-1 outsider Haverland, beating the likes of Olympic cycling champion turned jockey Victoria Pendleton.
"There are no words to describe this - I'm lost for words," Mellah said.
"When I passed the post I couldn't believe it, and then I saw all my family and friends and started crying. I am quite competitive, so I wanted to win this race, but I never expected to.