Bullock won for her role in "The Blind Side," while Streep also won for her performance in "Julie & Julia."
Related: See more photos of Sandra Bullock
"I'm really, really thrilled because I really love what I do," Streep said.
"It is a great honor to be in the company of the extraordinary women I was so lucky to be nominated with, because this one here," Bullock said, gesturing to Streep, "inspired me to do everything better."
Jeff Bridges scored the Best Actor award for his performance in "Crazy Heart," while "The Hurt Locker'" was named Best Picture.
Brad Pitt's "Inglorious Basterds" captured the trophy for Best Ensemble, plus, the film's writer/director Quentin Tarantino won for Best Original Screenplay. Also, James Cameron's sci-fi stunner "Avatar" was declared Best Action Movie and won a host of technical awards.
Video: Meryl and Sandra's lip-lock
- Dec. 13, 2017 2018 SAG Awards Nominees -- See their reactions