The tense exchange happened when they were critiquing Kree Harrison, who had just performed her first song of the night, "She Talks to Angels" by The Black Crowes.
Mariah liked the performance and said, "You can sing anything and I love to hear you sing." But she felt like Kree might have been trying too hard to perform: "My favorite Kree moments are when you are lost in a song and just don't care," she added.
Fellow judge Keith Urban agreed with Mariah's critique, but Nicki did not – and things went downhill from there.
"I disagree with Keith and Mariah," Nicki declared in her faux British accent. "That was the best performance of the night."
"I wasn't saying she was awkward," Mariah said as the two talked over each other. "You don't really disagree with me."
"No, I do," shot back Nicki. "And I'll explain."
Mariah started to speak again, but Nicki shut her down: "Simmer down, sir," she said.
Unlike the judges, the all-girl top five get along harmoniously and generally earned praise for their two performances each Tuesday night, first for a song from the year of their birth, and later for a song from their favorite diva.
Candice Glover kicked off the show and set the bar high with a super-confident, slowed-down version of former judge Paula Abdul's "Straight Up."
Mariah declared it "genius." Randy Jackson said she was "so in the zone," while Keith called it "so effortless," and likened her runs to a "slow wink across a bar"
Her night got even better when she brought all four judges to their feet after performing the Mariah's duet with Whitney Houston, "When You Believe."
Country girl Janelle Arthur sang "When I Call Your Name" by Vince Gill while strumming a guitar and earned positive remarks from three judges, though Keith admitted, "I didn't feel it." Later, her performance of "Dumb Blond" by Dolly Parton didn't wow the judges, with Nicki predicting she could be in danger of going home.
Kree's second song, Celine Dion's "Have You Ever Been in Love," was spectacular – all the judges agreed.
"You're not country, you're worldly. You're iconic," Nicki said. "You are Adele. You are Celine Dion. I'm having an epiphany right now while talking to you. You're everything."
Angie Miller earned similar praise for her two performances of the evening, particularly for her rendition of "Halo" by Beyoncé.
"Definitely top three," Keith predicted.
"Beyoncé is definitely going to hear about that performance," added Nicki.
Amber Holcomb's version of the Mariah cover "Without You" got mixed reactions from the judges. Keith called it "beautiful" and Mariah praised the choices she made in the song, but Nicki "wasn't impressed."
But Holcomb redeemed herself in Nicki's eyes when she belted out Barbra Streisand's "What Are You Doing The Rest of Your Life?" for the final performance of the evening.
"It was simply perfection," Nicki said. "You held every note like a classy diva should."
Mariah agreed with Nicki (this time!), saying, "Thank you for this performance."