The movie, which leads the nominees list with 7 nods, also saw Chazelle winning the best screenplay award.
The Globes, which kickstart the Hollywood award season, began with host Jimmy Fallon doing a hilarious parody of the much-loved movie, about two aspiring artistes finding romance in Hollywood.
The movie was soon won two Golden Globes back to back as it took the best original score award and was then named the winner of best original song for a motion picture.
Gosling, in an heartfelt speech, thanked his partner, Eva Mendes, for supporting him during the film while she was pregnant with their second child and caring for her sick brother.
"This isn't the first time I've been mistaken for Ryan Reynolds," he joked.
Aaron Taylor-Johnson of "Nocturnal Animals" registered a surprise win in the best supporting actor category beating British-Indian star Dev Patel of "Lion", Mahershala Ali for "Moonlight", Jeff Bridges for "Hell or High Water" and Simon Helberg for "Florence Foster Jenkins".
Best supporting actress trophy went to Viola Davis for "Fences".
Tom Hiddleston won best actor, limited series or TV movie "The Night Manager" while his co-stars Olivia Colman and Hugh Laurie won in the best supporting actress and actor categories, respectively.
French film "Elle", Isabelle Huppert, won the best foreign film.
"Zootopia" was named the best animated movie.