Morgan says this career milestone is "a miracle and a blessing" for "a mama from Knoxville, Tennessee" as she reflects on the show and her bond with her costars.
Morgan, who first gained recognition for her I'm Every Woman comedy special on Netflix a few years ago, stars in her very own sitcom, Leanne, that premiered July 31 and is already in the Top 10 list of TV shows on the streaming platform.
"I don't even know if I can describe it," Morgan tells PEOPLE in an exclusive interview of how it feels to reach this career high the same year she celebrates her milestone 60th birthday.
"I thought I was going to be younger and thinner, but that's okay," she jokes.
"I think if this had happened to me at 20, I don't know that I would've taken it well," she explains.
Morgan jokes that if the timing had been different and she was younger she "would've smoked a lot of cigarettes and done a lot of horrible things."
Co-star Kristen Johnston, who was beside Morgan for the interview, then chimes in, deadpanning, "She would've been in rehab with me."
Morgan plays a woman whose life is upended when her husband of 30-plus years leaves her for another woman while Johnston plays her twice-divorced sister who recently moved back home to the South from Chicago.
The duo agree that their sisterly bond was "instant."
"The minute we met, we bonded," Morgan says. "I go stand in her dressing room and stare at her as she's trying to rest. But I do, I love being with her and we had a ball."
Morgan credits the show's co-creator, Chuck Lorre, for recommending Johnston -- whom he worked with on Mom -- to play her sister as "the first thing he said to me."
"That is a good day for me," Johnston says of the praise.
"She's perfected the craft," he says of his newest star. "As stand-up comedy goes, when she's on stage, you know as the audience you're in good hands. This is going to be great."
Lorre admits he "never had any question that it would transfer over" from the stage to the screen, or that audiences would connect to and care about Morgan's character.
"That's something you can write down on a script, all the words in the world and all the jokes in the world, but you can't instill the feeling of empathy and compassion for a character. That comes from the actor or actress. It has to be built in," he explains. "It is very much part of who Leanne is."
As for Morgan, she is just soaking it all up.
"I'm a mama from Knoxville, Tennessee, and this happening for me, it's a miracle and a blessing," she says, getting emotional. "And honey, I still don't believe it."