"At times when I feel misunderstood, my fans always remind me that it's OK to be myself," she said.
Lana Del Rey appeared moved to be named international breakthrough act.
"This award means much more to me than you know," said the singer, who has gone from Internet-fueled buzz to backlash in record time after a disastrous performance last month on "Saturday Night Live."
Britpop icons Blur received a special prize for their contribution to music.
The four original members — Albarn, Graham Coxon, Alex James and Dave Rowntree — performed together for the first time since a series of concerts in 2009, offering versions of 1990s hits including "Girls & Boys" and "Parklife."
Most of the awards are chosen by more than 1,000 musicians, critics and record industry figures, with several decided by public vote.