Hamm had been nominated a stunning 16 times – eight for lead actor for his portrayal of Draper – before snagging his first Emmy win Sunday night.
Fittingly, the 44-year-old actor received a standing ovation as he crawled his way onto the stage.
"There's been a terrible mistake, clearly," Hamm joked while accepting the award.
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The Mad Men actor notably thanked ex-girlfriend Jennifer Westfeldt, whom he split with earlier this month after 18 years together, as well as their dog, Cora, during his speech.
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"It's incredible and impossible for me personally to be standing here so I want to thank the people to whom I owe an incredible debt," he said. "Cora and Jen, thank you all very much, I would not be standing here without you."
Hamm completed rehab earlier this year, explaining after he finished his rehab stint that "life throws a lot at you sometimes, and you have to deal with it as much as you can."
After the win, several of Hamm's costars seemed as thrilled about the award as Hamm himself.
"That was the thing I was most hoping for," said January Jones, who played first wife Betty Draper on the show, at the Governor's Ball. "He not only represents all of us but the body of work as a whole. It's so deserved and I'm so proud of him."
Kiernan Shipka, who played daughter Sally on the show, also said she was "just so pumped."
"I actually had snacks in my hands and had to hand them to my mom because I knew I'd have to jump up in a second. I knew! I'm just so proud of him," she said.
Costar Christina Hendricks simply said, "It was so nice to see him up there."
Hamm was up against Bob Odenkirk for Better Call Saul, Kyle Chandler for Bloodline, Kevin Spacey for House of Cards, Jeff Daniels for The Newsroom and Liev Schreiber for Ray Donovan.
Tina Fey presented the award at the Microsoft Theater in Los Angeles.
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Fox aired the 2015 Emmy Awards, hosted by Andy Samberg, live on Sept. 20.
With reporting by MELODY CHIU and PATRICK GOMEZ