They scooped two prizes at the US music industry awards - best rock performance for In My Place and best alternative album for A Rush Of Blood To The Head.
The 23-year-old star, who sings soft, jazzy songs, was shocked:
"I can't really explain why my record has done so well", she said.
Eminem, who won best rap album for The Eminem Show,
But Avril Lavigne's Complicated couldn't beat Norah's Don't Know Why to the Song of The Year award.
Foo Fighters took best hard rock performance for All My Life.