The American country singer, 22, was named Best Female Act and Best Live Act and also won Best Look out of five nominated categories.
"Drei? Drei? I can't believe you gave me three awards," she told the boisterous 7,000 strong crowd, trying out her best German.
Picking up the Best Look award for the most stylish act, Swift said: ''I am so excited I can't believe you gave me three awards.''
''I'm kind of insecure in general so this is great for my self-confidence".
She later posted on Twitter: "Such an insane night!!! You guys won me 3 EMAs! Best female, best live act, best look. Can't even begin to thank you enough. I love you!!"
The post was "re-tweeted" almost 10,000 times and "favourited" a further 6400 times.
Korean pop sensation Psy received the biggest reaction of the night when he played his breakout hit Gangnam Style complete with dozens of lookalike dancers.
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, after winning Best Video.
He thanked his fans and his family for living with ''a selfish job with a selfish guy''.
He added backstage: "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 added that his next album would have more English songs on it.
Rita Ora kicked off the show in spectacular style when she was lowered to the stage suspended in a cage before launching into a version of R.I.P.
She was followed by US pop band Fun who played their massive hit We Are Young, before Carly Rae Jepson performed Call Me Maybe.
The host, who this year filed for divorce from singer husband Seal, also teamed up with Psy for a tongue-in-cheek performance of the dance. "It was pretty," Psy said of the duet.
Reformed rockers No Doubt then performed their new single, and the cast of Geordie Shore named Justin Bieber the Best Male Act of the night.
The Canadian singer, who was not at the event, recorded a thank you message for his fans, saying: ''This is the greatest night ever''.
Other performances included The Killers who took to the stage to play Runaways.
Del Rey won the Best Alternative Act, beating Arctic Monkeys and Florence + The Machine to the award.
Rihanna, who led the nominations with six, failed to pick up a single award.
Boyband One Direction won Best New Act, before 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 Houston ''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.
There was also a video tribute to Beastie Boy Adam Yauch who died this year, before Swift closed the show with her huge hit We Are Never Ever Getting Back Together.
Swift embraced the concept for the show's finale, popping out of a magician's box and passing her top hat to a clown riding a miniature bicycle.
"I had a blast during the performance," Swift said. "All the circus acrobats and everything like that. It was so much fun."
Last year's awards in Belfast attracted 23 million viewers on all platforms, while this year's nominations attracted a record 184 million votes online and on mobile devices to decide the winners.
: Best Song - Carly Rae Jepson - Call Me Maybe
: Best New Act - One Direction
: Best Female Act - Taylor Swift
: Best Male Act - Justin Bieber
: Best Pop Act - Justin Bieber
: Best Live Act - Taylor Swift
: Best Hip Hop - Nicki Minaj
: Best Rock Act - Linkin Park
: Best Electronic Act - David Guetta
: Best Alternative Act - Lana Del Rey
: Best Video - Gangnam Style (Psy)
: Best Look - Taylor Swift
: Biggest Fans - One Direction
: Best Worldwide Act - Han Geng
: Best World Stage - Justin Bieber
: Best Push - Carly Rae Jepson
: Global Icon - Whitney Houston