The video for the track, which featured in the film Mandela: Long Walk To Freedom, was directed by Belfast artist Oliver Jeffers.
Jeffers, who now lives in New York, graduated from the University of Ulster in 2001 and has had his work displayed around the world.
U2 saw off competition from Coldplay, Justin Timberlake and Idina Menzel from Disney's animated hit Frozen to win the Best Original Song trophy during Sunday's award ceremony.
The song was written in honour of the late Nelson Mandela, who died in December.
Upon receiving the award, frontman Bono said: "This really is personal for us.
"This man turned our life upside down, right-side up, a man who refused to hate, not because he didn't have rage or anger or these things, but that he thought love would do a better job.
"We wrote a love song because it kind of is what is extraordinary about the film - it is kind of a dysfunctional love story.
"That's why you should see this film. You know about the global statesman, you don't know about the man, that's why you should see this film. We're good at the dysfunctional love stories."
U2 previously won a Golden Globe in the same category in 2003 for their song The Hands That Built America from Gangs of New York.
Often seen as a predictor to the Oscars, the major honours at the Golden Globes went to frontrunner American Hustle which won three awards, but 12 Years A Slave ended the night as best film drama.
Leonardo DiCaprio, a nine-time Golden Globe nominee, won his second Globe for best actor in a comedy for his uninhibited work in The Wolf Of Wall Street.
He thanked director Martin Scorsese for his mentorship and for "allowing me to stalk you to make this movie".
Alfonso Cuaron won best director for the space odyssey Gravity, while Cate Blanchett won best actress in a drama for her performance in Woody Allen's Blue Jasmine.
Golden Globe winners:
Best motion picture - drama - 12 Years a Slave
Best motion picture - musical or comedy - American Hustle
Best director - Alfonso Cuaron - Gravity
Best actor - drama - Matthew McConaughey - Dallas Buyers Club
Best actor - musical or comedy - Leonardo DiCaprio - The Wolf of Wall Street
Best actress - drama - Cate Blanchett - Blue Jasmine
Best actress - musical or comedy - Amy Adams - American Hustle
Best supporting actor - Jared Leto - Dallas Buyers Club
Best supporting actress - Jennifer Lawrence - American Hustle
Best screenplay - Her - Spike Jonze
Best original score - Alex Ebert - All is Lost
Best original song - 'Ordinary Love', Mandela: Long Walk to Freedom - Bono, The Edge, Adam Clayton, Larry Mullen, Brian Burton
Best foreign language film - The Great Beauty - Italy
Best animated feature - Frozen
Best TV series - drama - Breaking Bad
Best TV series - comedy - Brooklyn Nine-Nine
Best mini-series or motion picture made for TV - Behind the Candelabra
Best actor - drama - Bryan Cranston - Breaking Bad
Best actress - drama - Robin Wright - House of Cards
Best actor - comedy - Andy Samberg - Brooklyn Nine-Nine
Best actress - comedy - Amy Poehler - Parks and Recreation
Best actor - mini-series or motion picture made for TV - Michael Douglas - Behind the Candelabra
Best actress - mini-series or motion picture made for TV - Elisabeth Moss - Top of the Lake
Best supporting actor - series, mini-series or motion picture made for TV - Jon Voight - Ray Donovan
Best supporting actress - series, mini-series or motion picture made for TV - Jacqueline Bisset - Dancing on the Edge