He was crowned best new artist and also won the honours for best song, record of the year and best pop vocal album.
He triumphed ahead of household names such as Coldplay, Miley Cyrus, Ed Sheeran, Taylor Swift and Iggy Azalea at the ceremony in Los Angeles, where he was Grammy-nominated for the first time.
He even managed to eclipse superstars Beyonce and Pharell Williams, who won three awards each, compared to his quadruple whammy.
Smith, 22, performed Stay With Me, which won the song and record of the year titles, at the ceremony with Mary J Blige.
Accepting the record of the year trophy, he told the audience: “I want to thank the man who this record is about, who I fell in love with last year. Thank you so much for breaking my heart, because you got me four Grammys.”
Other big winners on the night included Beck, who was a surprise choice for the coveted album of the year honour, as well as best rock album. Pharrell Williams, who was honoured for best pop solo performance for his huge hit Happy, also won best music video for the song – which he performed live at the event – and best urban contemporary album for Girl.
Highlights of the ceremony included performances from heavy metal legends AC/DC, who kicked off the show with new single Rock or Bust and the classic Highway to Hell, and Madonna, who performed Living for Love dressed as a matador and surrounded by male dancers wearing bull masks.
Other British acts who took to the stage included Coldplay’s Chris Martin, who appeared with Beck; Sir Paul McCartney, who joined forces on stage with Kanye West and Rihanna; Eurythmics star Annie Lennox who sang along with Ireland’s Hozier, and Jessie J and Tom Jones, who performed a duet.
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Smith’s impressive night was reminiscent of the success of fellow Briton Adele at the ceremony in 2012, when she won four awards and attributed much of her success to songs written after a heartbreak.
London-born Smith has had a huge rise to prominence since the beginning of last year when he was named the winner of the BBC’s “Sound of 2014” poll of industry experts, which aims to highlight the best prospects for the year ahead. He was the only artist to sell more than a million albums in both the UK and the US for In the Lonely Hour.
He said: “Before I made this record, I was doing everything to try to get my music to the world. I tried to lose weight and was making awful music. It was only until I started to be myself that the music flowed.”
English pop star Ed Sheeran, who performed with ELO’s Jeff Lynne, left empty handed despite being nominated in both the best album and pop vocal album categories.
However, there was Grammy glory for British electronic act Clean Bandit, who won the best dance recording prize for Rather Be, while musician and composer Aphex Twin won best dance/electronic record for his first album in a decade, Syro.
Double-winner Beck said of his 12th album Morning Phase: “We made this record at my house for the most part, so I would like to thank my kids for letting me keep them awake a little bit longer.”
The late US comic Joan Rivers won her first Grammy, in the spoken word category, for Diary of a Mad Diva, five months after her death. Her daughter Melissa Rivers, who collected the trophy, said: “If my mother was here tonight, she would not only be honoured and thrilled to be holding her first Grammy, she would most likely have it copied and on the air on QVC by 11.”
The Grammys turned serious when president Barack Obama, in a recorded message, called on musicians and fans to pledge to stop domestic violence. “It’s not OK and it has to stop,” he said. “Artists have a unique power to change minds and attitudes and get us thinking and talking about what matters.”
Domestic violence victim Brooke Axtell followed, taking the stage to share her experience as a survivor and to urge others to recognise their worth and seek help to save themselves. Her life was saved, she said, when she sought help at a domestic violence shelter.