The Rock's Ballers on HBO was nominated for Outstanding Sound Editing for a Comedy or Drama Series.
HBO has led the nominations for the last 17 years.
"It has been another exceptional year in television marked by extraordinary storytelling from a wealth of diverse and innovative content creators", said Washington.
In the heavyweight drama category, "Game of Thrones" will vie against "The Crown", the final season of "The Americans", "Stranger Things", "This is Us", "Westworld", and last year's victor, "The Handmaid's Tale".
Others in the category include black-ish, Silicon Valley, 'Curb Your Enthusiasm and Unbreakable Kimmy Schmidt.
Rhys and Brown will be up against Brown's castmate Milo Ventimiglia, along with Jason Bateman for "Ozark" and Ed Harris and Jeffrey Wright for "Westworld".More news: Super-mum Serena ready for royal date with Meghan at Wimbledon
The variety series category also left "The Tonight Show" on the sidelines for the second consecutive year, deservedly so, given that Jimmy Fallon's brand of vanilla-flavored latenight comedy feels a little too tepid for the times.
The series, which will not air this year, is in contention for the Emmy for Best Drama Series along with The Crown, The Americans, The Handmaid's Tale, Stranger Things, This Is Us and Westworld.
HBO awards darling "Veep" was ineligible this year and its crown passed to "Atlanta", the FX comedy created by and starring Donald Glover, which amassed 16 nods. If he wins, he will earn the coveted EGOT, having previously won a Grammy, Oscar, and Tony.
Hit PLAY on the video above to watch the Emmy nominations announced live, then drop a comment with your thoughts on the nominees below.
The 70th annual Primetime Emmys will air September 17 from the Microsoft Theater in Los Angeles.