The Brit, who plays scientist Stephen Hawking in The Theory Of Everything, beat the Birdman star in the most outstanding actor category in Los Angeles.
Redmayne, who has already won a Golden Globe, dedicated his win to those such as Hawking who live with ALS, also known as Lou Gehrig's disease, for their “triumph of spirit”.
Visibly shocked and at times emotional during his speech, he told the audience he had learned a lot when making the film.
“I would like to dedicate this award to those people around the world living with ALS, to those who have lost their lives to this brutal disease,” he said.
“In preparing to play Stephen I met many people fighting ALS, and I met their families fighting alongside them. And the courage and the bravery and the spirit, this triumph of spirit that I witnessed, blew my mind. So I'm incredibly grateful to them.”
SAG award winners in full British television programme Downton Abbey took the title of best ensemble cast in a drama series for the second time, while Birdman's award for best ensemble cast featured English actress Andrea Riseborough.
Honorary Briton Kevin Spacey, who has been artistic director of London's Old Vic theatre for more than a decade, won best actor in a drama series for House of Cards.
At next month's Academy Awards, Redmayne will go head to head with fellow British actor Benedict Cumberbatch, who plays code-breaker Alan Turing in The Imitation Game, as well as Steve Carell, nominated for Foxcatcher, American Sniper's Bradley Cooper and Birdman's Keaton.