The ABC comedy beat the two series - and Nurse Jackie, The Big Bang Theory and Glee - to take home the prize for 'Comedy Ensemble' at the ceremony in Los Angeles.
The show's star Jesse Tyler Ferguson, who joked that he had been "elected to speak for the group", paid tribute to the other series during the cast's acceptance speech.
"We are so honoured to be nominated against the brilliant casts of Glee, Nurse Jackie, Big Bang Ratings, uh, Theory," he quipped. "But also I think we'd be doing the evening a great disservice if we didn't mention the brilliant departing casts of 30 Rock and The Office.
Copyright: WENN FayesVision/WENN.com"You all have set the comedy bar so high, and if we can be just half as brilliant and smart and wonderful as you are, then we've succeeded."
Ferguson continued: "We're all fans of yours - except for Aubrey [Anderson-Emmons, the 5-year-old who plays Lily]. She has no idea who you guys are! But if we can absorb any of you into our cast, if you need jobs, please call our casting director Jeff Greenberg."
Ferguson concluded the cast's speech by describing the award - their third consecutive win - as a "huge honour", adding: "We love being actors. You've been so generous - thank you."
Watch Modern Family's acceptance speech at the SAG Awards below: