The three-piece from Kilmarnock were not the only Scottish winners, as Calvin Harris scooped Best Dancefloor Anthem for his song Sweet Nothing featuring Florence Welch.
Rock veterans the Rolling Stones were double winners more than half a century after they first featured in the magazine's pages.
The group was named Best Live Band, and their documentary Crossfire Hurricane the best film.
Chart-topping stars One Direction were named Worst Band, while singer Harry Styles was declared Villain of the Year.
The Killers were handed the Best International Band prize.
Former Smiths guitarist Johnny Marr took NME's Godlike Genius award.
And The Cribs – for which Marr was briefly guitarist – took the prize for Outstanding Contribution.
Given To The Wild by Maccabees took the award for Best Album.