The New Jersey rockers walked away with 'Best International Band' and 'Best Video' for 'Na Na Na (Na Na Na Na Na Na Na Na Na)', which they also performed at the ceremony in London on Wednesday night.
Other acts to triumph included Muse, who were named 'Best British Band' for the second year running, and Arcade Fire, who scooped 'Best Album' for The Suburbs.
Recent Brit Award winner Laura Marling was crowned 'Best Solo Artist', Hurts were given the 'Best New Band' accolade, and Biffy Clyro triumphed in the 'Best Live Band' category.
There was also recognition for Justin Bieber, who was named 'Least Stylish' and awarded the 'Worst Album' trophy for My Worlds 2.0.
In the non-music categories, Inception won 'Best Film, Skins won 'Best TV Show' and Lady GaGa and David Cameron were awarded the 'Hero' and 'Villain' awards respectively.
Highlights of the show will be broadcast on Saturday on Channel 4 at 11.25am and later at 11.20pm.
> Click here for a full list of winners from this year's NME Awards