Sharing photos from the evening on her Instagram Story, Kazan shared a couple's shot originally posted by stylist Leith Clark where the actress posed with Dano.
"Mom and dad are so damn cute," the stylist wrote.
Another shot paid attention to Kazan's recent haircut, writing, "a dress worth cutting your hair to show off (those shoulders)."
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In addition to their 3-month-old, the couple also shares a daughter born in 2018.
The actress, 39, put her baby bump on display in October, when walking the red carpet with Dano for Kazan's film, She Said at the 60th New York Film Festival at Alice Tully Hall, Lincoln Center.
The Big Sick star also showed her bump on the cover of Marie Claire's Power Issue alongside Mulligan and journalists Jodi Kantor and Megan Twohey.
Speaking to Marie Claire about balancing motherhood and her work as an actress, Kazan admitted that it can be "really hard to balance your priorities."
"Everyone talks about work-life balance, but it's also really hard to balance your priorities," she shared. "I wanted to be the person who took my daughter to her first day of preschool, and I couldn't do that because I felt like this job, this work was as important as that. And vice versa."
Lauren Dukoff/Marie Claire
"I was just really relieved to read a script where that was represented and where I could put that part of myself in there," she added of her work on She Said. "And I felt really bolstered by having [Megan and Jodi] and [their] experiences and Carey [Mulligan] and her experiences. It made me feel not alone."
Kazan and Dano first met when they appeared on stage together in the 2007 play, Things We Want, and have been together for over a decade. The pair have also maintained a relationship on screen.
The couple has collaborated on multiple projects, including the 2012 film Ruby Sparks. For the film, the couple shared the films leading roles and Kazan wrote the screenplay. Dano commented about working with his longtime partner on the film during a 2012 interview with The New York Times.
"For me, the best thing that Zoe did was not write a film about our relationship or write us as characters," Dano said. "Calvin and Ruby are Calvin and Ruby, they're not Paul and Zoe."