Maisel", which also won the comedy series Emmy, is "about a woman who's finding her voice anew and it's something that's happening all over the country right now.
Peter Dinklage took home the award for Best Supporting Actor in a Drama Series at the 2018 Emmys for his performance as Tyrion Lannister on HBO's Game of Thrones. "Mrs. Maisel" also won four other awards, including the best actress for Rachel Brosnahan.
Borstein actually received two Emmy nods this year, with her Supporting Actress trophy bolstered by a win for Outstanding Character Voice-Over Performance thanks to her work on Family Guy.
More than 40 years on from his first nomination, this was his first win.
Criss won Lead Actor in a Limited Series for his portrayal of Andrew Cunanan in The Assassination of Gianni Versace, and he said that accepting the award was the "most extraordinary moment of my life thus far".
"Come Back, Barack", a sketch that was featured on a November "Saturday Night Live" episode hosted by Chicago's Chance the Rapper, won for original music and lyrics.
Rachel Brosnahan won the comedy actress Emmy at the 70th annual awards on Monday.
Outstanding Supporting Actor in a Comedy Series goes to Henry Winkler, for his role in Barry. But he took his talent to new heights, using his acceptance speech to pop the question to girlfriend Jan Svendsen. "If you stay at the table long enough the chips come to you".
Earlier this year, the series won two Golden Globes.
"Game of Thrones" is back and led the nominations with 22 nods, including outstanding drama against last year's victor, "The Handmaid's Tale".
"Thank you to Netflix for your support of artists", Jeff Daniels, a supporting actor victor for Godless, said as he accepted his award. The Saint Ignatius College Prep grad noted that his wife refused to join him at the Emmys because she didn't want to watch him lose.
The show opened with a daring song-and-dance number poking fun at myriad controversies including diversity in Hollywood.
Oh played along from her seat: "Thank you, but it's an honor just to be Asian", said the Korean-Canadian actress.
Yawning, alas, was the involuntary response to most of the rest of the Emmy show, produced by Saturday Night Live impresario Lorne Michaels, who made the unfortunate call of placing his Weekend Update hosts Colin Jost and Michael Che front and center.