The group collected the gong live on BBC Four, telling a record executive who was disparaging towards them in their early days because they “look different”: “F**k you.”
Visions of a Life had been the joint fifth favourite with bookies ahead of tonight’s ceremony, which took place in London.
The record had sold just over 50,000 copies before tonight – and is expected to see a healthy boost in figures after this evening.
According to bookies, Nadine Shah was the frontrunner to take the trophy – her album Holiday Destination was given the edge by outlets such as Ladbrokes, who installed her as the 3/1 one-to-beat.
Narrowly behind her on 4/1 were Sons Of Kemet with Your Queen Is A Reptile and King Krule was on 5/1 with The Ooz.
Elsewhere, Jorja Smith iswaspriced at 7/1 for Lost & Found, Arctic Monkeys were on 10/1 with Tranquility Base Hotel & Casino, along with Wolf Alice.
Everything Everything were on 12/1 with A Fever Dream, with Florence + The Machine’s High as Hope on 16/1 and Everything Is Recorded’s eponymous collection on 20/1.
Lily Allen’s No Shame and Noel Gallagher’s High Flying Birds’ album Who Built The Moon? were both on 25/1, along with Novelist Guy by Novelist.
Judges for the prize included broadcasters Clara Amfo, Danielle Perry and Mistajam; musicians Ella Eyre, Jamie Cullum, Lianne La Havas and Marcus Mumford; journalists Harriet Gibsone, Phil Alexander and Will Hodgkinson; Radio X head of music Mike Walsh and 6Music and Radio 2’s head of music Jeff Smith.
The Mercury Prize began back in 1992, with last year’s gong going to Sampha with Process.
Other recent winners have included Skepta, Benjamin Clementine, Young Fathers, James Blake and alt-J.
Happening across town will be PopJustice’s Twenty Quid Music Prize, which started as a tongue-in-cheek alternative to the Mercury back in 2003.
That ceremony will reward the artist of the year’s best pop song with a £20 note, and has been won in the past five times by Girls Aloud and three times by Little Mix.
Contenders this year include Gabrielle Aplin, George Ezra, Rita Ora, Rae Morris, All Saints, Calvin Harris and Dua Lipa, Clean Bandit featuring Demi Lovato, Tracey Thorn, Naughty Boy with Ray BLK and Wyclef, Metroplane and Bree Runway, Let’s Eat Grandma and CASISDEAD.
The Mercury Prize airs on BBC iPlayer or BBC Four at 9pm or BBC 6 Music from 7pm.