Zendaya, 24, became the youngest lead drama actress winner for her role as a troubled teenager in "Euphoria."
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"I know this seems like a really weird time to be celebrating," Zendaya said. "But I just want to say there is hope in the young people out there. I know our TV show doesn't always feel like a great example of that," but thanked young people out there "doing the work."
"Succession," a family power struggle over a media empire, was honored as best drama series, and creator Jesse Armstrong used the opportunity to offer "unthanks," including to President Donald Trump for what Armstrong called his "crummy" handling of the pandemic.
SEE ALSO: Full list of Primetime Emmy winners, nominees
Highlights of 2020 Emmy nominations
"Succession" star Jeremy Strong won the drama actor trophy for his role as an aspiring heir.
The awards for Pop TV's "Schitt's Creek" included best comedy series and trophies for its stars, including Catherine O'Hara and father-son Eugene and Daniel Levy.
"It is absolutely incredible. I think my dad said it best earlier this evening: it's a dream you don't want to wake up from, to be honest. What an absolutely unbelievable way to end our series," Daniel Levy said backstage.
In his acceptance speech, he said the sitcom was about "the transformational effects of love and acceptance, and this is something we need more now than ever before," encouraging people to register and vote to achieve that goal.
Other winners, including "Watchmen" star Regina King, made a point that the Nov. 3 general election was near.
Watch Regina King's Emmys acceptance speech
All the winners accepted their awards virtually in the pandemic-safe ceremony, including O'Hara, but she wasn't alone.
"Though these are the strangest of days, may you have as much joy being holed up in a room or two with your family as I had with my dear Roses," O'Hara said, surrounded in a decorated room by mask-wearing co-stars who play the Rose family members.
Levy called it "ironical that the straightest role I ever played lands me an Emmy for a comedy performance. I have to seriously question what I've been doing" for the past 50 years.
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Moments later, his son won the award for comedy writing for "Schitt's Creek" episode, then shared a directing award and captured the supporting actor comedy trophy. The supporting actress trophy went to his co-star Annie Murphy.
Daniel Levy thanked his father and O'Hara for teaching an extended "master class" in comedy. The show's sweep came for its much-acclaimed final season.
References to coronavirus were an ongoing part of the ceremony, with essential workers - including a teacher and a UPS deliveryman - presenting awards and Jason Sudeikis ostensibly getting a COVID-19 test onstage.
In a year with a record number of Black nominees, 35, there was a notable lack of diversity in the show's early going. With "Schitt's Creek" gobbling up comedy awards, that left "Insecure" and creator Issa Rae empty-handed Sunday.
That was also true of Ramy Youssef, creator-star of the semi-autbiographical comedy "Ramy," about a young Muslim American's love and religious life. Yousef tweeted a video of a haz-mat suit-wearing person clutching an Emmy and waving goodbye after he lost the lost the comedy actor category.
There was a sign of change with the drama awards, which came in the latter part of the ceremony.
The powerful series "Watchmen," a graphic novel-adaptation steeped in racial pain, was voted best limited series and King won lead actress for her work on the HBO show. She was showered by confetti as she accepted in an armchair, wearing a T-shirt that honored police shooting victim Breonna Taylor.
"This is so freaky and weird," said King, who regained her composure and called on viewers to vote and, backstage, explained why she wore the message shirt.
"The cops still haven't been held accountable," she said. "She represents just decades, hundreds of years of violence against Black bodies. Wearing Breonna's likeness and representing her and her family and the stories that we were exploring, presenting and holding a mirror up to on 'Watchmen,' it felt appropriate to represent with Breonna Taylor."
Her co-star, Yahya Abdul-Mateen II, won the Emmy for best supporting actor in a limited series. Uzo Aduba won the counterpart actress award for her portrayal of Shirley Chisholm in "Mrs. America."
Watch Uzo Aduba's Emmys acceptance speech
Anthony Anderson, a nominee for "black-ish," came on stage to make his disappointment vigorously known, saying the awards should have been "Howard University homecoming Black."
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"This isn't what it should have been. ... But Black stories, Black performances and Black Lives Matter," he said, urging host Jimmy Kimmel to shout with him.
Tyler Perry, the actor turned media mogul, accepted the Governors Award.
Supporting drama awards went to Billy Crudup for "The Morning Show" and repeat winner Julia Garner for "Ozark."
"Last Week Tonight with John Oliver" was again honored as best variety-talk series, with David Letterman announcing the award after being abandoned roadside by an annoyed ride-share driver.
Oliver joined the ranks of winners calling for Americans to vote, as did Mark Ruffalo, who won the limited series acting trophy for "I Know This Much is True"
Kimmel opened the show with a monologue that appeared to be defiantly delivered in front of a packed, cheering theater - until it was revealed they were clips from past Emmy shows.
"Of course I'm here all alone. Of course, we don't have an audience," he said. "This isn't a MAGA rally. It's the Emmys."
Watch Zendaya's Emmys acceptance speech
With more than 100 long-distance video feeds with nominees ahead, "what could possibly go right?"
A minor gaffe marred Saturday's virtual Emmys for technical and other honors, when Jason Bateman's name was announced for a guest acting award that belonged to Ron Cephas Jones of "This Is Us." Other guest acting honors went to Eddie Murphy and Maya Rudolph for "Saturday Night Live" and Cherry Jones for "Succession."
Bateman was one of the few people on hand at the Staples Center for Sunday's show, sitting in the audience during Kimmel's opening monologue. Bateman sat stone faced amid a collection of cardboard cutouts, trading jokes with Kimmel after the host pointed out he was there.
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