Barman Niall Sexton, 22, from Londonderry impressed the panel with his performance of Gravity by Sara Bareilles.
And Conor McGinty, 21, also from Londonderry, got the thumbs up with his rendition of Say Something by A Great Big World.
The success stories came after a rocky start to the episode for singing hopefuls.
The first four auditions, including 19-year-old potato farmer Jordan Devine and Bono lookalike Peter Richard, resulted in four Nos.
Cowell’s young son Eric also made an appearance on the show, visiting his dad backstage to present him with a painting.
Controversial singing duo Ottavio and Bradley have made it through to the next round of The X Factor, despite a resounding “No” from Simon Cowell.
The bandmates initially auditioned separately after a row over uncooked chicken but were encouraged to reunite and sing together by the judges, with Sharon Osbourne telling them: “You could be double trouble.”
The duo performed the Pussycat Dolls’ hit Buttons to the delight of judge Nicole Scherzinger, but that was not enough to win over Cowell, who told them: “I’m glad you made up, but you weren’t great individually. I think you are worse together.”
However, the pair still secured the thumbs up from the other three judges and sailed through to boot camp.
Kayleigh Marie Morgan, 19, a student from Clydach, near Swansea, was a hit with all four of the judges. She dazzled the panel with her rendition of With You from Ghost.
Judge Louis Walsh hailed her as a “powerhouse”, while Scherzinger told her: “I’m scared of you in the best way. You were born to do this.”
Also winning the judge’s approval was Janet Grogan, 28, from Dublin, who was a familiar face for Cowell. She made it to his Six Chairs in 2014 but he eventually swapped her for another singer. He later said he had made a mistake and regretted the decision.
After she performed Pillowtalk by Zayn Malik in Saturday’s episode, Cowell said: “I was always praying you would come back into the audition room.” Grogan was then awarded a Yes from all four.
The X Factor continues on Sunday at 8pm.