Swift won the awards for Best Female Act, Best Live Act and Best Look Sunday night, and Bieber, who did not attend the ceremony, was named Best Male Act and Pop Act and winner of the World Stage Award.
The British-Irish pop group One Direction won the awards for Best New Act and the Biggest Fans.
Canadian singer Carly Rae Jepsen took home the Best Song prize for "Call Me Maybe" and South Korean singer Psy earned the Best Video statuette for "Gangnam Style."
America's Alicia Keys accepted the Global Icon award on behalf of late singer Whitney Houston, who accidentally drowned in a hotel bathtub last February after using drugs.
Supermodel Heidi Klum served as host of the MTV EMAs show.