The trio, who starred in the hit 2006 film, presented the award for best male actor in a comedy series during the 30th annual ceremony in Los Angeles on Saturday night.
Streep, wearing a burgundy long-sleeved Prada dress, appeared to fall into the microphone on stage before saying: "Two things, I forgot my glasses, clearly, and the envelope", before Blunt and Hathaway appeared on stage with both items in a nod to their previous film roles.
In the film, Streep played Miranda Priestly, the demanding editor-in-chief of a high fashion magazine, with Blunt as her long-term assistant Emily Charlton and Hathaway as new assistant Andrea Sachs.
"Meryl and Miranda Priestly are sort of like twins," Blunt said, to which Streep strongly disagreed.
"No, no. That wasn't a question," Hathaway told Streep, in a nod to an infamous Miranda line.
Blunt also quoted Miranda, telling Streep: "By all means move at a glacial pace, you know how that thrills me."
The Lord of The Rings' Sean Astin (L) and Elijah Wood presented a SAG award together. (AP PHOTO)
The Lord Of The Rings co-stars Elijah Wood and Sean Astin also reunited on stage to present the award for outstanding performance by a female actor in a supporting role.
Astin, who played Samwise Gamgee, revealed why Wood, who played Frodo Baggins, never received his SAG Award trophy after the hit film picked up a gong two decades ago.
Astin said: "It's been 20 years and yet I'm sorry you couldn't be there that night."
Wood joked about their win, saying: "Sean, you were supposed to collect my statue for me if we won, what happened to it?"
"Well, it's somewhere. If, by somewhere, you mean frodo-fan-7-11's shelf because he bought it on eBay. Sorry," Astin joked.
The awards ceremony also brought the cast of Modern Family back together to present a trophy. (AP PHOTO)
The cast of Modern Family also reunited on stage with stars Sofia Vergara, Julie Bowen, Ty Burrell, Eric Stonestreet, Jesse Tyler Ferguson and Ed O'Neill taking aim at their lives after the hit show aired its final season.
Vergara praised the recent success of her Netflix show Griselda, while O'Neill admitted he missed the money Modern Family brought and Stonestreet joked that he could call Kansas City Chiefs tight end Travis Kelce from the stage.
