Swift, who picked up four nominations, had watched from her seat throughout the ceremony as rivals Lambert and Lady Antebellum went up to the stage. She was stunned when her name was finally called for the final prize, a fan-voted honor.
"This is the first time that I've ever won this and I'm just losing my mind," Swift said, as she fought back tears.
Lambert retained her crown as top female vocalist and her wistful tune "The House That Built Me" was honored for single, song and video of the year at the 46th annual awards ceremony.
The award for single goes to the artist and producer, whereas the trophy for best song is given to the artist and composer.
Lambert, a 27-year-old Texan, went into the ceremony with a leading seven nominations, including two in the video category.
The country trio Lady Antebellum won trophies for album and vocal group of the year and Brad Paisley was named top male vocalist for the fifth consecutive year. The award for top new artist went to The Band Perry, a sibling trio from Mississippi.
The announcement of winners took second place to a string of performances divided between two hotel venues, the MGM Grand and Mandalay Bay. The winner of the first award was not revealed until almost an hour into the three-hour ceremony.
(Reporting by Dean Goodman in Los Angeles and Tim Pratt in Las Vegas; Editing by Paul Simao and Bill Trott)
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