Alt-J were announced as winners of the Mercury Prize
The group, who met at Leeds University in 2007, looked stunned as they collected the award - despite being the bookies' favourites as the ceremony got under way.
They picked up the Â£20,000 prize at the event at the Roundhouse, in Camden, north London, which was hosted by Lauren Laverne and screened in a brief five-minute slot on Channel 4.
Accepting the award on stage, the band - Thom Green (drums), Joe Newman (guitar/vocals), Gwil Sainsbury (guitarist/bassist) and Gus Unger-Hamilton (keyboards) - said there were too many people to thank.
They said: "We might just thank everyone on team Alt-J who has ever made a difference." They also thanked their parents for "not making us get jobs".
Speaking backstage, Gus said the Â£20,000 prize money would not change their lives too much. He said: "It won't nearly pay off our student loans." But he admitted to being a fan of his own work, saying: "I like listening to it and I think that is a testament to it, it's the same four guys."
Joe said the band would take their parents out for dinner but would also celebrate in more traditional rock star style.
He said: "We're going to go and get really p*****, we've just won a Mercury. Christ, I'm going to stay out and carry this as long as I can."
They beat acts including rapper Plan B to win the award and singer-songwriter Richard Hawley, who missed out again - six years after losing to Arctic Monkeys.