The US singer was named Best Female Act and Best Live Act as well as picking up the prize for Best Look.
Picking up the Best Look award for the most stylish act, Taylor said: "I am so excited I can't believe you gave me three awards." She added: "I'm kind of insecure in general so this is great for my self-confidence."
Justin won another award when he was named Best Pop Act, while Linkin Park won Best Rock Act.
The award for Best Hip Hop act went to Nicki Minaj, and David Guetta won Best Electronic Act. Lana Del Rey won the Best Alternative Act, beating Arctic Monkeys and Florence + The Machine to the award.
Boyband One Direction won Best New Act, before Alicia Keys picked up the Global Icon Award on behalf of the family of the late Whitney Houston and praised the singer's "incredible ability to captivate and mesmerise us".
She told the audience Whitney "was my home girl, my friend" before introducing a tribute video which included messages from One Direction and Lady Gaga.
The Jonas Brothers handed the Best Worldwide Act to Chinese singer Han Geng. The Best Video award was won by Gangnam Style singer Psy, who thanked his fans and his family for living with "a selfish job with a selfish guy".