Darren Criss Gives Loving Shout-Out to His Fiancée as He Wins Emmy Award: 'My Darling'

Congratulations are in order for Darren Criss!

The star took home the 2018 Emmy Award for outstanding lead actor in a limited series or movie for his starring role in The Assassination of Gianni Versace: American Crime Story.

“Oh my God, you guys are witnessing the most extraordinary moment of my life thus far,” he said before thanking creator Ryan Murphy.

The actor held back tears as he thanked his family for their support. “Unlike the character I play, I was lucky enough to be raised in a home that was loving.”

Criss also gave his fiancée Mia Swier a sweet shout-out.

“My darling Mia, you roll the windows down and pump the music up in my life,” he said.

Along with Criss, the nominees were John Legend (Jesus Christ Superstar Live In Concert), Antonio Banderas (Genius: Picasso), Benedict Cumberbatch (Patrick Melrose), Jeff Daniels (The Looming Tower), and Jesse Plemons (Black Mirror, USS Callister).

Check out all of PEOPLE’s 2018 Emmys coverage here

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TVLine recently reported that Criss, who earned his first Emmy acting nomination for his role as killer Andrew Cunanan in FX’s The Assassination of Gianni Versace: American Crime Story, was favored to win the outstanding lead actor award. (He was previously nominated for an Emmy in 2015 for writing the song “This Time” for the Glee finale.)

Criss, 31, previously opened up to PEOPLE about taking on the role of the serial killer known for shooting the Italian fashion designer on the steps of his Miami mansion and murdering four other men in 1997.

“I had a friend tell me when I got the part, ‘You’re playing the gay boogeyman,’ ” he said. “I was like, ‘Excuse me?’ He was like, ‘When he was on the run, we would all spook each other [by saying] Andrew Cunanan is going to come get you.’ The things that are said about him in the show aren’t crazy.”

When it came to playing Cunanan, Criss wanted to make sure he was portraying all of the complex aspects of his character, which included everything from killing in cold blood to singing Laura Branigan’s “Gloria” at the top of his lungs in his car.

“Human beings are so complex,” he said. “We are capable of so many different emotions and the reasons behind those emotions. I’m not asking people to empathize or pardon anything that Andrew has done, but I do like people unconsciously figuring out how much they can relate to this person whether how little or how much.”

The 70th Primetime Emmy Awards, hosted by Michael Che and Colin Jost, are airing live from the Microsoft Theater in Los Angeles on NBC.