In a first for the EMAs, which were created in 1994, MTV announced categories stripped of gender in a bid to "break barriers".
The Irish band dedicated the award to label boss Chris Blackwell of Island records, who signed them nearly 40 years ago.
Eminem's new single 'Walk On Water' featuring Beyonce is getting all kinds of reactions from the audience. The night's big victor, Mendes, sung his best song-winning track "There's Nothing Holding Me Back" from a huge light box.
Cuban-American singer Camila Cabello was honoured with the best pop prize, while Coldplay snatched the best rock award.
The awards are held in a different European city each year, with winners selected by fans across the continent.
Louis Tomlinson, from the boy band One Direction, landed the best United Kingdom and Ireland act. The rapper picked up the best hip hop gong. Other multiple nominees include Sheeran, Sam Mendes and Kendrick Lamar.
U2 were crowned the Global Icon, with Bono singing a burst of Stormzy's "Blinded By Your Grace" as they collected the trophy.
U2, who played an MTV-sponsored concert in London's Trafalgar Square on Saturday, received the Global Icon award from Leto, who said "U2 changed my life".
It marks the third time the awards will be held in Spain, but the first time it will take place in Bilbao.
"I'm so confused why is Rita Ora walking down the red carpet in a dressing gown and towel around her head?"
The cable channel also runs the Video Music Awards which are renowned for top performances and the occasional controversy, including pop diva Lady Gaga wearing a dress made of meat to the ceremony in 2010.