Eurovision: Come Together saw the public vote for their favourites, on the night that this year's song contest was due to take place.
The 2020 competition was cancelled in March amid the coronavirus pandemic.
The Swedish foursome won it in 1974 in Brighton. The track, which topped the UK charts and set them on their way to fame, went on to sell nearly 6m copies.
Speaking later on the night, Bjorn Ulvaeus from the band said he found it "hard to believe" that was where it began for them all those years ago.