Anne Hathaway and Tina Fey were also honoured during Sunday night's (January 27) ceremony at the Shrine Exposition Hall in Los Angeles.
> Screen Actors Guild Awards: Movie winners at 19th annual ceremony
Silver Linings Playbook actress Lawrence, who almost tripped up over a chair on her way to the stage and was seen adjusting her dress as she took to the podium, recalled the day that she received her SAG membership card in the post at the age of 14 during her acceptance speech.
Describing the moment as "the best day of my life... because it put me in a category with all of you", Lawrence thanked David O Russell, saying: "I think I speak for many of us when I say you've helped more than your son [with this movie]."
It was earlier revealed that Lawrence has pneumonia.
> Lincoln's Daniel Day-Lewis: 'My son thought I worked in construction'
Daniel Day-Lewis was honoured for Lincoln, and credited friends Leonardo DiCaprio and Liam Neeson with encouraging him to take the role when he was initially having doubts.
Day-Lewis also joked that when he recalled that an actor assassinated Lincoln, "it's only fitting that every now and then an actor tries to bring him back to life again".
> Screen Actors Guild Awards: TV winners at 19th annual ceremony
Breaking Bad star Cranston won his first Actor statuette for 'Drama Actor', thanking Vince Gilligan for writing "the role of my career" in his acceptance speech.
Additionally thanking his "brothers and sisters in SAG who have endowed me with this wonderful award", Cranston quipped: "Tonight, at least, I am well-endowed."
> 'Argo', 'Homeland' win at Producers Guild of America Awards 2013
Danes added a Screen Actors Guild trophy to her growing collection of awards for Homeland, noting in her acceptance speech that her agent cautioned she would "have a lot to do" if she accepted the role of Carrie Mathison.
She also paid tribute to her co-stars including Damian Lewis and Mandy Patinkin, and said that Morena Baccarin "runs my lines with me almost every night while making dinner for me".
Les Misérables star Hathaway added to her Golden Globes success by taking home the prize for 'Female Actor In A Supporting Role', and Tommy Lee Jones won the 'Male Actor In A Supporting Role' accolade for Lincoln.
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Kevin Costner and Julianne Moore added to their Emmys and Golden Globes with victories in the 'TV Movie or Miniseries' categories for Hatfields & McCoys and Game Change respectively.
Alec Baldwin and Golden Globes co-host Fey were also recognised for their roles in 30 Rock.
The ensemble casts of Argo, Downton Abbey and Modern Family also triumphed, along with the stunt teams from Skyfall and Game of Thrones.
> 'Argo's Ben Affleck laughs off Oscar snub
Golden Globe-winning director Ben Affleck - speaking for the cast of Argo - joked that maybe he would become a better actor for standing in the same spot that Day-Lewis had been in moments earlier.
"The people you see on stage, you have more than 150 actors... the one thing they had in common was that... they wanted to kill it to make the movie better. Because that's what actors do all over the world every day... we are in your debt," Affleck added.
Dick van Dyke was also honoured with a Lifetime Achievement Award during the telecast.
Photo gallery - SAG red carpet: