Among her prizes were best female artist, best streaming song for Shake It Off and the ceremony's top honour, artist of the year.
Sam Smith won best new artist and accepted his trophy via a video message using a series of cards.
One Direction came away with two trophies, for best group and best touring artist, dedicating one of the awards to Zayn Malik, who left the band in March.
Other Brit winners were Coldplay who won best rock album for Ghost Stories, while Irish singer Hozier picked up best rock song for Take Me To Church.

The judge, who chairs the inquiry, said in an article in the Observer it must strike a balance between the rights of accusers and the accused.
But she also dismissed claims it would mainly focus on famous people.
The inquiry is examining how public bodies handled their duty of care to protect children from abuse.
In the article she said a number of commentators "have in past weeks spoken out, inaccurately, about the Independent Inquiry into Child Sexual Abuse, which I chair and the way in which the inquiry will conduct its work. I'd like to correct those inaccuracies."
It comes after the former conservative MP Harvey Proctor, who was cleared of being part of a Westminster paedophile ring, criticised Justice Goddard for suggesting the inquiry would consider the actions of the police from the standpoint of victims and survivors.
Mr Proctor, 69, had his home raided and was questioned as part of Operation Midland but it was found there was insufficient evidence even to justify a prosecution being considered.
He claimed it "irreparably ruined my life" and said that to review investigations from just the victims' standpoint lacked judicial balance.
But Justice Goddard promised the inquiry will hear evidence from those affected by false allegations of abuse, recognising the damage that can be caused.
"Those who have claimed recently that the inquiry will consider only the perspectives of victims and survivors, and exclude those of others affected by allegations of child sexual abuse, are wrong," she said.
"As I announced last November, the inquiry intends to explore the balance that must be struck between encouraging the reporting of child sexual abuse and protecting the rights of the accused."
Justice Goddard added that the inquiry had already announced 13 investigations to date, most of which "do not relate to individuals of public prominence".
The inquiry is examining allegations of past and ongoing failures to protect children in schools, children's homes, secure accommodation and local authority care.
It will also look at the responses of institutions, including the police, health service, the Crown Prosecution Service and religious bodies to allegations of child sexual abuse as well as investigating broader issues, such as the role of the internet in facilitating abuse.
In the past three weeks preliminary hearings into four investigations have taken place including those looking into Lambeth Council, Rochdale Council and the Anglican Church.

16 February 2017 Last updated at 08:27 GMT
The four pups are from Newquay Zoo in Cornwall and they are learning how to swim.
The four young Asian short-clawed otters are being taught by their parents and four uncles.
They were born in October last year and we think they're otter-ly gorgeous!
Taylor Swift dominated at the Billboard music awards winning eight of the 14 categories in which she was nominated.
[NEXT_CONCEPT]
The public inquiry into child sexual abuse will not ignore the damage done to prominent people who were falsely accused, Justice Lowell Goddard says.
[NEXT_CONCEPT]
How cute are these otter pups?