Lawrence, 22, fended off strong competition from Jessica Chastain and 86-year old French actress Emmanuelle Riva for the Best Actress prize.
"You guys are just standing up because you feel bad that I fell down," she said, after tripping on her way up the stairs to the stage where she accepted the award.
"But thank you," she added, clutching the statue. "This is nuts."
Lawrence plays a young woman who becomes a sex addict after the death of her husband, and then strikes up an unlikely romance with a bi-polar former teacher played by Bradley Cooper.
The role proved the versatility of the young actress, whose film work has ranged from independent dramas to big budget action fare like "X-Men: First Class" and "The Hunger Games," in which she plays heroine Katniss Everdeen.
Lawrence also won Golden Globe and Screen Actor's Guild awards ahead of Sunday's Oscars. She won her first Oscar nomination for her break-out performance as a teen trying to keep her dysfunctional family together in the 2010 independent film "Winter's Bone."
Producers of "Silver Linings Playbook" initially felt Lawrence was too young to play the feisty widow, but she struck up an endearing chemistry with Cooper's character, Patrick.
Lawrence was born in Louisville, Kentucky, and started her career at the age of 14 with small roles in film, television and in commercials.
She soon moved with her family to Los Angeles where acting jobs came steadily and in 2010 she was named one of Variety magazine's Top Ten Actors to Watch.
Lawrence's swift rise to the top has made her a hot commodity in the fashion world and celebrity magazines, where she regularly turns heads on the red carpet.
In December she was named the world's "most desirable woman" by website AskMen after rising from the No. 47 spot a year earlier.
She is a regular face on the front covers of magazines like Vogue and in October she became the new face of Christian Dior's Miss Dior brand of handbags.