As HBO Celebrates a Big Night, Questions About Its Future Loom

Not far away at the Amazon party, a rival in the battle for streaming supremacy was celebrating.

It was a boisterous, loud and sweaty affair at the Chateau Marmont. There was Jon Hamm accidentally stumbling into the photo booth area. Stephen Colbert, Jane Lynch and Amy Sherman-Palladino, the creator of “The Marvelous Mrs. Maisel,” made the rounds. The man responsible for the entire operation, Amazon’s chief executive, Jeff Bezos, was sequestered in a reserved corner of the party space. He stood with his son and a stream of well-wishers who needed permission from the two bodyguards manning the area to get through to shake his hand.

But he was not the star of the night. The ’90s hits blaring from the D.J. booth were no match for the applause that erupted when Phoebe Waller-Bridge, the star and creator of “Fleabag,” made her way into the party, with her boyfriend, the writer-director Martin McDonagh, in tow. From the second she walked in, Ms. Waller-Bridge was so besieged by well wishers that she could barely get a bite of food or even light her cigarette.

No wonder. “Fleabag” upset the HBO awards show juggernaut “Veep” for best comedy and Ms. Waller-Bridge claimed three Emmys over all. She beat Julia Louis-Dreyfus to win best actress in a comedy, the first time in the show’s seven seasons that Ms. Louis-Dreyfus did not win.

“We had a great night,” said Mr. McDonagh. “I was hoping for one. Who knew?”

Amazon has had the reputation in Hollywood for being a sleeping giant. It spends plenty and it has seemingly infinite resources, but, despite the earlier success of shows like “Transparent,” its overall impact has been muted.

Now, between “The Marvelous Mrs. Maisel” and “Fleabag,” it has back-to-back Emmy comedy winners. And it is a sign that there are plenty of competitors — particularly from the tech world — ready to go toe to toe with HBO.

With all that, HBO is not pushing the panic button just yet.

“I have the benefit of being here for 15 years so I’ve heard this over and over again,” said Casey Bloys, HBO’s president of programming. “This is the world we live in and our formula of curation and betting on people we believe in and doing the hard work, it pays off. I’m not going to say I’m not worried. You can’t do this job without being worried. But I feel really good about the future.”