They were named artists of the year and also took home album of the year and favourite pop/rock album.
"This has been a real perfect day... America feels like a second home to us," said Liam Payne.
Katy Perry, who did not appear at the ceremony in Los Angeles, also won three awards, including one for best single for Dark Horse featuring Juicy J.
The awards, many of which are decided by a fan vote, also saw Taylor Swift speak out again in defence of traditional models of music distribution.
The singer, who was presented the Dick Clark award for excellence by Motown musician Diana Ross, thanked fans for acknowledging her campaign.
"What you did by going out and investing in music and albums is you're saying that you believe in the same thing that I believe in - that music is valuable and that music should be consumed in albums, and albums should be consumed as art and appreciated," she said.
After the release of 1989, Swift removed all of her albums from Spotify, saying the streaming service devalued music and did not pay artists enough.
Iggy Azalea beat the likes of Eminem and Drake to the title of favourite rap/hip hop artist.
"This award is the first award I've ever won in my entire life, and it means so much to me that it is for best hip hop because that's what inspired me to move to America and pursue my dreams, and it's what helped me when I was a teenager to escape and to get through my life and to better times," the 24-year-old said.
"And it means so much that I can stand here against Eminem and Drake and come out with this."
Calvin Harris and Sam Smith took home favourite artist awards in the EDM and pop/rock categories. Frozen was named best soundtrack.
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The 29-year-old helped the Bears win the One-Day Cup last season, scoring 257 runs at an average of 64.25 in 10 appearances in the competition.
Evans joined Warwickshire in 2010 and also won the County Championship in 2012 and the T20 Blast in 2014.
Sussex head coach Mark Davis described Evans as "player of great ability".
He added: "He plays in all formats of the game and is a brilliant acquisition for the club. I believe Laurie's best years are in front of him, and he is driven to achieve his undoubted potential."
Evans has predominantly played white-ball cricket for Warwickshire, but has scored 2,926 runs at an average of 34.02 in first-class cricket.
He had a spell on loan with Northamptonshire in 2016.
Bears first-team coach Jim Troughton said: "Laurie has played an important part in our white-ball cricket for several years, but has been unable to secure a regular place in the team for first-class cricket.
"Whilst it's naturally disappointing that Laurie has decided that he no longer wants to play for Warwickshire, we do not wish to stand in the way of his ambitions in the game and we wish him the very best in his career with Sussex.
"We are also aware that he has been keen to move closer to his family in London and being based on the south coast will work better for him."

17 July 2016 Last updated at 19:25 BST
Arriving into Belfast International Airport on Sunday morning, most of them told BBC News NI reporter Claire Graham they were happy to be home.
One Direction have topped the winners list at the American Music Awards, taking home a total of three prizes.
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Sussex have signed batsman Laurie Evans on a three-year contract after Warwickshire released him a year early from his deal at Edgbaston.
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Northern Ireland holidaymakers returning from Turkey have been giving their reaction to the attempted military coup on Friday.