Natalie Portman won best actress for her portrayal of former first US lady Jackie Kennedy in Jackie.
Casey Affleck was named best actor for his role as a troubled caretaker in Manchester by the Sea.
The best original screenplay award was tied between Chazelle for La La Land and Kenneth Lonergan for Manchester By The Sea.
Viola Davis was the recipient of two awards
Chazelle paid tribute to Gosling and Stone as he collected the best picture award.
He told them: "Both of you (gave) more than I ever could have expected from actors... just the most transformative
performances I`ve ever been lucky enough to film."
La La Land`s other wins included best song and best score.
The film opened in just five cinemas in North America this weekend, grossing $855,000 (£678,464) for Lionsgate, according to box office estimates. The $171,000 (£135,751) average per cinema is an all-time record for a film opening in so few cinemas.
Viola Davis was named best supporting actress at the Critics` Choice Awards for her role in Fences, which explores race relations in 1950s America.
She was also given the inaugural See Her Award, which honours actresses who redefine the portrayal of women in the media, after becoming the first black woman to win the Emmy for best actress in a drama last year.
Mahershala Ali won best supporting actor for his role in coming-of-age film Moonlight.
American Crime Story: The People Versus OJ Simpson collected four awards
Disney film Zootopia won best animated feature.
Like the Golden Globes, the Critics` Choice Awards also honour television.
British stars Thandie Newton and James Corden both picked up awards - Newton for best supporting actress in a drama series for Westworld, and Corden for best talk show for his Late, Late Show.
Evan Rachel Wood won best actress in a drama series for her role as robot Dolores in Westworld.
John Lithgow was named best supporting actor in a drama series for his turn as Sir Winston Churchill in The Crown, the Netflix drama about the Queen.
American Crime Story: The People v OJ Simpson won four awards, including best film made for TV or limited series.
`Not funny`
Courtney B Vance - who played Simpson`s lawyer Johnnie Cochran - won best actor in the same category, while Sarah Paulson was named best actress for her role as prosecutor Marcia Clark.
Sterling K Brown picked up best supporting actor for his performance as prosecutor Christopher Darden.
Game Of Thrones was named best drama series, while Silicon Valley picked up the best comedy series prize.
Alec Baldwin was named best guest performer in a comedy series for his turn as Donald Trump on Saturday Night Live.
It comes after the US president-elect tweeted that the sketch show is "totally biased, not funny and the Baldwin impersonation just can`t get any worse".
Comedian TJ Miller hosted the awards show in Santa Monica, California, two days after he was arrested for allegedly slapping a cab driver.
He made no reference to the alleged incident.
