The country superstar beat contenders including Adele, who had the year's best-selling album with "21" and led all nominees with four.
Swift told the audience "This is crazy!" as she picked up her award.
It was her third win of the night. She also won favorite country album and favorite country female artist.
Maroon 5 and Taylor Swift had the right moves at the American Music Awards: The band led and the country princess picked up the first trophies at Sunday's ceremony.
Nicki Minaj might need to change her hair color to gold.
The pink-loving hip-hop diva picked up two trophies Sunday at the American Music Awards. Minaj kicked off the fan-favorite ceremony by sporting a pair of speakers on her much-talked about posterior. She was later honored as favorite rap/hip-hop artist, besting a group that included mentor Lil Wayne, and won favorite rap/hip-hop album for "Pink Friday."
"There's so much love in this room," beamed the pink-haired Minaj.
Maroon 5, still riding high off their comeback hit "Moves Like Jagger," won for favorite pop-rock band/duo/group.
"I'd also like to thank our incredible fans for making this happen," said lead singer and "The Voice" judge Adam Levine as he and the rest of the band picked up their trophy.
Swift won country female artist.
Nicki Minaj launched the 39th annual fan-favorite ceremony with a performance featuring tethered back-up dancers, stilt-walking robots and super-producer David Guetta emerging from behind a pillar of speakers. The pink-haired singer - wearing a pair of speakers on her much-talked about posterior - kicked off the show with "Turn Me On" before launching into "Super Bass."
She later won rap/hip-hop artist, besting a group that included her mentor, Lil Wayne.
"Oh my god, you guys, there's so much love in this room," Minaj said, who also thanked Taylor Swift, a big fan of her "Super Bass" hit.
Adele leads the nominees with four nods at this year's AMAs, which honor music artists based on online votes.
Other top nominees include Katy Perry, Lady Gaga, Lil Wayne, Rihanna and The Band Perry, who have three bids apiece.
Other performers were Justin Bieber, who got in the holiday spirit with "Mistletoe," Kelly Clarkson, who performed a swinging version of hit "Stronger," and Chris Brown, who sand a ballad before breaking out into his signature dance moves.---