The $150,000 (pounds 92,000) Grawemeyer Award for Music Composition, the most lucrative of its kind, is offered in recognition of outstanding achievement by a living composer. Bainbridge beat 181 other entrants to become only the second Briton to win the prize, the other being Sir Harrison Birtwhistle in 1987.
According to the critic Paul Driver, the award is the musical equivalent of a Nobel Prize. "This award has gone to the most illustrious names in the world and it is fitting that Simon has won. He is not glamorous but his work is shocking and profoundly original."
Bainbridge, 44, received the award yesterday from the University of Louisville in Kentucky for his work Ad Ora Incerta, a stirring setting of the poetry of Primo Levi written in late 1945 and early 1946, only a few months after he was released from the Auschwitz death camp.
Bainbridge said the idea of using Levi's poetry first came to him while he was browsing in a New York bookshop a decade ago.
"I found a book of his poetry and I felt it had an instant musical resonance. It is darkly melancholic poetry and I hope the music reflects that."
The work was commissioned by the BBC in 1995, but has only been heard once, on its premiere in March of that year when the BBC Symphony Orchestra was conducted by the composer himself.
After winning the Grawemeyer, Bainbridge's publishers are hopeful it will be heard again, ideally at next year's Proms. "His breakthrough has really come in the last two years, when he has been writing some really wonderful compositions," said Catherine Manners, of Novello Music Publishers.
Bainbridge has been described by a prominent critic as "the best British composer alive". He studied at the Royal College of Music, where he currently holds a teaching position, as well as one at the Guildhall School of Music and Drama.
Over 25 years he has developed a list of critically-acclaimed works, including Double Concerto commissioned by the Cheltenham Festival and Landscape and Memory for the London Sinfonietta; Ad Ora Incerta is for solo mezzo-soprano, bassoon and orchestra.
The award, established by the American businessman and philanthropist H Charles Grawemeyer, is particularly prized by musicians because it is given for a specific composition.