American country singer Swift, who left the Country Music Association awards empty-handed less than two weeks earlier, picked up honours for Best Female, Best Live and Best Look.
"Drei? Drei? I can't believe you gave me three awards," Swift, who was nominated in five categories, told the crowd of 7,000, trying out her best German.
One of the night's most popular performers was dance sensation Psy with his record-breaking hit Gangnam Style, which won Best Video.
Skipping through the venue and on to the main stage in a sparkly blue jacket with his horse riding-inspired dance, he became the first South Korean artist to perform at the annual awards.
"This is beautiful. This is my very first time to participate, perform, be nominated, as an Asian artist, as a Korean artist, so I don't know what to say," he said.
Host Heidi Klum teamed up with Psy for a tongue-in-cheek performance.
Rihanna, who led the nominations with six, failed to pick up a single award.
Canadian teen heartthrob Bieber matched Swift's tally, claiming Best Male for the second year in a row as well as Best Pop and Best World Stage.