White was named best comedy actor for his role as Chef Carmy, a man trying to turn his family's Chicago sandwich shop into a fine dining establishment.
"This show has changed my life and instilled a faith that change is possible," White said as he held his award on stage at the Peacock Theater in downtown Los Angeles on Sunday.
Moss-Bachrach, Cousin Richie on "The Bear," won supporting comedy actor for his role as a restaurant manager and father.
"I'm so grateful for this show and to work with these beautiful people," Moss-Bachrach said as he thanked his castmates.
Both had won the same awards at the last Emmys, which was held in January after Hollywood labour strikes disrupted the normal schedule.
Billy Crudup landed his second Emmy for supporting actor for a drama for playing a conniving media executive in "The Morning Show". (known as "Morning Wars" in Australia). He motioned to his "piece of eye candy there, my wife" - fellow nominee Naomi Watts - as he held his trophy, and acknowledged the team behind the news drama.
"This process has been incredible for me," he said.
Billy Crudup has won the Emmy for outstanding supporting actor in a drama series. (AP PHOTO)
"Schitt's Creek" stars Eugene and Dan Levy shared hosting duties at the red-carpet ceremony, the first father-and-son duo to emcee the awards.
"If things go south, my name is pronounced Martin Short," Eugene Levy deadpanned, referring to the "Only Murders in the Building" star who was in the audience.
Dan Levy joked that the Emmys were known as "broadcast TV's biggest night for honoring movie stars on streaming services."
"Shogun," a historical epic set in feudal Japan, headed into the ceremony as the frontrunner to take the night's top trophy for best drama series.
"The Bear" was expected to be named best comedy again, according to awards pundits.
HBO's "Hacks," about a 70-something comedienne and a millennial writer, could play the role of spoiler in the comedy category. Due to the timing of their seasons, the shows have never competed head-to-head at the Emmys.
Winners were chosen by the nearly 22,000 performers, directors, producers and other members of Hollywood's Television Academy.
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