Hurd and Morris, both country music singers, performed the duet "Chasing After You" during Wednesday's episode of the NBC late-night talk show.
Hurd and Morris performed the song on a dimly-lit stage. The couple faced each other as they sang about being stuck in a cycle with a love interest who keeps leaving and coming back.
"Yeah, every time, every time you say we're done / You come back to the love you were running from / Don't know why, don't know why I let you but I do / Guess I love chasing after you / I love chasing after you," the pair sing.
Hurd released "Chasing After You" as a single in February. The song marks Hurd and Morris' first duet.
"We've written a lot of songs together, and for each other, but this is kind of the first time we've stepped out in this way," Hurd said on CBS This Morning following the song's release.
"It really reminded me of Ryan and my story getting together when we first met," Morris added.
Hurd and Morris married in March 2018 and have a 13-month-old son, Hayes Andrew.
In an interview on The Ellen DeGeneres Show this week, fellow country music singer Luke Bryan laughed off reports he fathered Morris' baby. The Sun had published an article in April that said Morris "gave birth to her first child with her husband Luke Bryan."
"So, I'm having coffee, and my mother calls me and she goes, 'I'm sitting here reading some gossip thing,'" Bryan recalled. "And then she goes, 'It says you fathered Maren Morris' child. I go, 'Oh my gosh. I do not need this today.'"
At the time, Bryan had recently released the song "Waves," which was co-written by Hurd.
"I am not the father," Bryan said before joking, "We can call Maury Povich or however y'all want to go about it."
"Chasing After You" is Hurd's first release since his EP EOM EP, released in June.