"I just want to say thank you. This is completely unexpected. Congratulations to all the other nominees and thank you to everybody involved with the show," Baldwin said upon collecting the first prize presented at the evening's event.
Moments later, Fey won her SAG award.
"I'm very surprised. I share this with the cast of '30 Rock' and the writers, and I want to thank some of my acting teachers because I actually did have some," Fey said. "I just want to take a moment to say to everyone at NBC, 'We are very happy with everything and happy to be there.'"
Fey was referring to the recent shakeup at the network that ended with "The Tonight Show" host Conan O'Brien leaving his post after seven months because NBC announced it planned to move the show to 12:05 a.m. to make way for "The Jay Leno Show."
The show lost the award for best ensemble of a comedy series, however, to the cast of "Glee."
"This is unreal," "Glee" co-star Jane Lynch told the audience. "We couldn't be happier to be acting on this show and to be chosen by our peers means the world to us."
Notable deaths of 2014 [PHOTOS]