Bieber was another multiple winner, picking up best pop act and top male singer.
Much of the attention in the run-up to the awards has been on the 17-year-old, who has denied allegations made by a US woman that he fathered her child when he was 16.
Accepting the second of his awards, he said: "There's been a lot of crap talked about me lately, but I've pulled through."
The cherubic pop star had earlier avoided media questioning, declining even to pose on the red carpet with his girlfriend, host Selena Gomez, when they arrived for the awards.
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It's difficult to deal with a highly competitive colleague. Every time you submit work, they try to find ways to outperform you. Although you have no interest in pitting your talent against theirs, this other person thinks very differently. Ignoring them won't be possible. A good way to disarm this pest is to invite them out for coffee. Describe what you've observed and ask for a truce. Irrational people are often thrown off balance when their behaviour is addressed in a direct manner.More