Matt Healy and his band, who picked up the Best Album and Best Group prizes, were also among the night's performance highlights at the ceremony, which Hugh Jackman opened with an ambitious set, inspired by his film and hit soundtrack "The Greatest Showman".
Meanwhile, Harris was named British Producer of the Year and also won British Single of the Year for his "One Kiss" collaboration with Dua Lipa, who teamed up with Sam Smith and Rag'n'Bone Man to perform a megamix of the DJ's hits.
Upon accepting the award, band member Jade Thirlwall said, "We never win this! Oh my God, thank you so much! We have had absolutely no shame in asking people every day to vote for this."
There were also wins for Tom Walker (British Breakthrough Act), and Ed Sheeran (Global Success Award), while Drake, Ariana Grande and The Carters - aka Beyonce Knowles and Jay-Z - picked up the international gongs.
Pink, who became the first non-Brit to land the Outstanding Contribution to Music award, closed the show with a lengthy medley of her hits.
The full list of winners is: