The success, in the face of competition from bands such as Blur and Biffy Clyro, is all the more impressive because the Stones played only a few shows last year, including two UK gigs at the O2 in London. It makes up for the band's failure at the Brit awards, where they lost in the same category to Coldplay.
As the Stones were given the award, Ronnie Wood said: "I feel really grateful after all the hard work that we put in – it's got to be fucking live, baby! We've only waited 50 years for it."
The band is contemplating further shows this year, with Ronnie Wood saying he intends to "twist [his bandmates'] arms" into playing Glastonbury.
They also won the NME award for best music film, for their documentary Crossfire Hurricane. They had been further nominated for music moment of the year and best book, the latter for 50, an anthology of photographs. The awards were voted for by NME readers.
Wood was the only member of the band to attend the ceremony, at the Troxy in east London. A spokesman said: "All the accolades this band have thrown at them over the years stem from one thing: on that stage they continue to be quite magnificent – the ultimate bar band, who deliver every time. They're well chuffed to be honoured with these awards as they come from real music fans, not a committee."
Florence Welch was the other big winner of the night, picking up the awards for best solo artist and best dancefloor anthem for Sweet Nothing, her song with Calvin Harris.
The former Smiths guitarist Johnny Marr, who recently released his debut solo album, won the godlike genius award – past recipients include Noel Gallagher and Dave Grohl.
Wood presented Marr with his award and said "What a great guy. I've known him since he was a tiny chap. It's well deserved."
Marr said: "The NME and I go back a really long way. And any 15 or 16 year olds who want to be in a band reading about this on the bus or at college next week, keep going, it's the best job in the world and it really matters."
In a video tribute to Marr, Noel Gallagher said: "He can't be imitated as a guitarist. He can play those riffs like it's the most natural thing in the world – and it is for him."
Marr was also a member of the Cribs between 2008 and 2011, and the remaining band members, the three Jarman brothers, won the outstanding contribution to music award. Ryan Jarman told the Guardian: "It's the kind of award you imagine someone like Queen might get, not us."
Mike Williams, the NME editor, said: "The Brits have their place, but we like to think of our awards as the best rock'n'roll party of the year, and age is no barrier. Johnny Marr has had a fantastic career and the Stones still appear to be completely relevant to our audience."
One Direction were voted worst band, and Harry Styles was named villain of the year, seeing off David Cameron and dubstep producer Skrillex among others.
Biffy Clyro were named best British band, and the new band award went to Palma Violets.
There were also awards for best fan community, won by Muse, and best Twitter, which went to Alana Haim – aka @babyhaim – from the band Haim.
Biffy Clyro, Foals, Miles Kane and Paul Weller and the Cribs performed live, before Marr was joined by Wood and the Vaccines frontman Justin Young for a set to close the evening.
The first NME awards were held in 1953, a year after the music paper was first published and a full decade before the Rolling Stones' recording debut. That year Ted Heath and his group won for best dance band and Ronnie Scott picked up the outstanding musician award.
The NME awards 2013 winners
Godlike genius Johnny Marr
Teenage Cancer Trust outstanding contribution award The Cribs
Best British band Biffy Clyro
Best album Given To The Wild, The Maccabees
Best international band The Killers
Best track Inhaler, Foals
Best TV show Fresh Meat
Best music film Crossfire Hurricane, the Rolling Stones
Best re-issue 21, Blur
Best solo artist Florence Welch
Best new band Palma Violets
Best music video R U Mine?, Arctic Monkeys
Best festival Reading & Leeds
Best live band The Rolling Stones
Best dancefloor anthem Sweet Nothing, Calvin Harris featuring Florence Welch
Philip Hall Radar award Child Of Lov
Best Twitter Alana Haim, Haim
Best book The Story of the Streets, Mike Skinner
Music moment of the year Olympics opening ceremony
Hero of the year Barack Obama
Villain of the year Harry Styles
Best small festival Festival No 6
Worst band One Direction
Best fan community Muse
Best film The Hobbit: An Unexpected Journey
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