Adams, 39, won for her role as an accent-swapping con artist while Lawrence took home the evening's first award for her work as a bitter, unintentionally funny housewife.
"I don't know why I am so scared, I am sorry," a visibly flustered Lawrence, 23, said during her speech, thanking director Russell, after saying how she admired his work.
It was Russell, who also directed Lawrence in her Globe and Oscar-winning role last year in 'Silver Linings Playbook'.
The best actor in a comedy or musical trophy went to Leonardo DiCaprio, 39, for his role as a hedonistic broker in Martin Scorsese's 'The Wolf of Wall Street'.
The actor was amused to get his career's second Globe in the comedy category. DiCaprio praised Scorsese for their fifth collaboration, saying, "Thank you for your mentorship."
'12 Years a Slave', a compelling and unique peek into the terrors of slavery, took home the award for best film - drama.
Directed by Steve McQueen, the film stars Chiwetel Ejiofor as Solomon Northup, a free black man in 1840s New York who is sold into slavery.
Cate Blanchett took home the award for best actress in a motion picture - drama for her role of a broke neurotic woman in Woody Allen's 'Blue Jasmine'.
The 44-year-old actress has two previous Golden Globes, for playing Queen Elizabeth I in 1998 Shekhar Kapur directed 'Elizabeth' and Bob Dylan in 2007's 'I'm Not There'.
Blanchett topped Sandra Bullock ('Gravity'), Judi Dench ('Philomena'), Emma Thompson ('Saving Mr Banks') and Kate Winslet ('Labor Day') for the award.
Matthew McConaughey took home the award for best actor in a motion picture - drama for 'Dallas Buyers Club' beating the likes of Chiwetel Ejiofor ('12 Years a Slave'), Idris Elba ('Mandela: Long Walk to Freedom'), Tom Hanks ('Captain Phillips') and Robert Redford ('All Is Lost').
This is McConaughey's first Globe nomination or win. The actor lost considerable amount of weight to portray an AIDS victim.
Mexican filmmaker Alfonso Cuaron was crowned best director in a closely contested list for his work on the outer space thriller 'Gravity', beating the likes of Russell, McQueen ('12 Years a Slave') and Spike Jonze ('Her').
Spike Jonze won for his original screenplay for quirky, futuristic romance 'Her', about a man who falls in love with the voice of his computer's operating system.
Jared Leto won best supporting actor in a motion picture for playing a transgender woman with AIDS in 'Dallas Buyers Club'.
Alex Ebert won for best original score for 'All Is Lost'. Best song honours went to 'Ordinary Love', U2's song for 'Mandela: Long Walk to Freedom,' which was picked up by Bono and the Edge. 'Frozen' won best animated film. And Italy's 'The Great Beauty' won in the best foreign film.
Woody Allen was honoured with the Cecil B DeMille Award but, as expected, the director was a no-show. Actress Diane Keaton, who earned a Globe and an Oscar for lead actress for Allen's 1977 classic, 'Annie Hall', collected the honour on behalf of the award-shy filmmaker.
"I think it's safe to say that Woody Allen is an anomaly," Keaton said in her tribute.
Tina Fey and Amy Poehler did not disappoint during their second year hosting the Golden Globe Awards.
"This year is legit," said Fey at the start of the show, referring to the level of star power in attendance.
The awards show at the Beverly Hilton in Los Angeles marked a good send-off for TV series 'Breaking Bad'.
The acclaimed drama about a high school teacher turned ruthless meth maker, which ended its run last fall, won best drama, and the show's star, Bryan Cranston, who plays Walter White, won best actor. It was the first Globe for the show and Cranston.
Poehler won for best actress in a comedy series for 'Parks & Recreation'. Robin Wright won her first Golden Globe for best actress in a drama series for the political drama 'House of Cards'.
Jon Voight, 75, won the Golden Globe for best supporting actor in a series, miniseries or TV movie for the drama series 'Ray Donovan'.
New comedy 'Brooklyn Nine-Nine' won in the best television series-comedy or musical award, while lead actor Andy Samberg also won for best actor in a TV comedy as wacky detective Jake Peralta.
'Behind the Candelabra', HBO's drama about flamboyant pianist Liberace and his young boyfriend, won best miniseries or TV movie.
Elisabeth Moss won her first ever Golden Globe for best performance by an actress in a TV miniseries or movie for the thriller 'Top of the Lake'. Jacqueline Bisset won a best supporting actress trophy for the TV miniseries 'Dancing on the Edge'.