Swift, 25, one of the top-selling musical acts in the United States last year, also picked up awards for top female artist, top Billboard 200 artist and album and top hot 100 artist, among others.
Swift, whose video of her latest single “Bad Blood” premiered at the awards, also took home a special achievement award chosen by fan voting.
“This is such a good night,” Swift enthused as she collected the night’s big prize, top artist. Earlier, after winning top Billboard 200 album for “1989,” she said “you guys embraced change, embraced me doing something new. I’ll never forget it.”
Swift and Smith competed directly in several top categories, with Swift prevailing. Smith, 22, who had received 13 nominations to Swift’s 14, also won for top radio songs artist.
The British band One Direction was another multiple winner, winning top touring artist and top duo or group, while Iggy Azalea was a triple winner for top rap artist, rap song and top streaming artist.
Rock band Van Halen opened the show with a throwback performance of their hit song “Panama,” while Hozier later performed his smash hit “Take Me to Church.”
Other musical highlights included Kelly Clarkson’s “Invincible,” Britney Spears and Iggy Azalea who let loose with “Pretty Girls” and Nicki Minaj rapping “The Night is Still Young.” Little Big Town also teamed up with Faith Hill for their hit song, “Girl Crush.”
Pharrell Williams swept the R & B categories, taking honors for song, album and artist while Jason Aldean took the prizes for top country song and album. Florida George Line was named top country artist.
Hozier won top rock artist and top rock song, while Coldplay took the award for top rock album.
The awards, hosted by rapper Ludacris and supermodel Chrissy Teigen, were handed out in a live broadcast from the MGM Grand Garden Arena in Las Vegas.
Billboard magazine, which covers the music industry, said the finalists were based on fan interactions with music, including album and digital sales, touring, radio airplay, streaming and interactions on social media websites and other online sites for music.