"When you have to pick up your dog's poop every day, it's very grounding," the actress, 35, told PEOPLE preshow correspondent Alicia Quarles.
Then the subject turned to her boyfriend, NFL star Aaron Rodgers, 32, who stepped into the spotlight with the actress at the Academy Awards but waited patiently as she gave solo interviews.
"And it's the people you keep around you," she said of how she stays down to earth. "My boyfriend's super chill and easygoing." (He's also affectionate! When he wasn't chatting with fellow NFL vet Michael Strahan, Rodgers squeezed her hand lovingly before one of Munn's interviews.)
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Despite being red carpet official in picture-perfect ensembles – Munn went with a sleek orange dress while Rodgers kept it classic in a tux – the couple isn't quite ready for a trip down the aisle. In January, The Newsroom star shut down engagement speculation in a text message thread with her mom, a screenshot of which she shared on Instagram.
Check out PEOPLE's full Academy Awards 2016 coverage and complete winners list!
That same month, she told PEOPLE her mom wasn't the only loved one reading all the reports about her high-profile relationship with the Green Bay Packers quarterback.
"I didn't know anything about it until I started getting all these texts and calls from people," she told PEOPLE. "I was getting emails from relatives that I haven't spoken to in a long time, aunts and uncles, just like, 'Can we come to the wedding?' "
With reporting by ELIZABETH LEONARD and PATRICK GOMEZ
The 88th annual Oscars, hosted by Chris Rock, are being presented live on ABC from the Dolby Theatre in Hollywood, California.