In her multiple acceptance speeches on Sunday, Swift did not mention the glitches that disrupted Ticketmaster's sales for her upcoming tour last week, prompting the company to apologize to her late on Friday.
Other honors for Swift on Sunday included favorite pop album, country album and video for her re-recording of 2012 record "Red." The singer has been remaking albums from her past because of a dispute with her former record label.
For artist of the year, Swift triumphed over formidable names including Beyonce, Harry Styles, The Weeknd, Drake, Adele and Bad Bunny, who had gone into the night with a leading eight nominations. The Puerto Rican rapper and singer received two awards, for favorite male Latin artist and favorite Latin album for "Un Verano Sin Ti."
Pop singer Pink opened the AMAs show dancing and singing on roller skates to her upbeat song "Never Gonna Not Dance Again." Later in the ceremony, she performed "Hopelessly Devoted to You" in a tribute to Olivia Newton-John, the "Grease" singer who died in August.
Musician Lionel Richie, known for "All Night Long" and other 1980s hits, was celebrated with the AMA's icon award. Stevie Wonder and Charlie Puth performed a medley of Richie songs on dueling pianos.
Dove Cameron, a former Disney Channel actress who reached the Billboard charts this year with the pop single "Boyfriend," was named best new artist.
Comedian and host Wayne Brady rapped in his monologue at the start of the show. "Ain't nobody getting slapped tonight," Brady joked, referencing Will Smith's infamous attack on Chris Rock at the Oscars.