The award was Cuaron's first Golden Globe on his first nomination.
The director spent four years working on the film, which he wrote with his son Jonas. The film's setting brought plenty of technical challenges.
To portray stars Sandra Bullock and George Clooney floating through space, Cuaron and his team strapped the actors into mechanized rigs that could spin them around on command, while a camera was similarly mounted on a giant robotic arm.
In the end, the technical achievements helped Cuaron to beat out Paul Greengrass for the hijacked-at-sea thriller "Captain Phillips," Steve McQueen for the biographical drama "12 Years a Slave," Alexander Payne for the father-son road movie "Nebraska," and David O. Russell for the Abscam-inspired con story "American Hustle."
Many consider the Globes' director prize to be a more exclusive filmmaking honor than that of best picture, because the category contains just five nominees. Best picture is split into two prizes — drama and comedy or musical.