Father Ray Kelley was told his rendition of REM's Everybody Hurts on Saturday evening's show was one of Simon Cowells' "favourite ever auditions".
The judge and TV producer added: "I thought your voice was beautiful, I loved the version of the song, this was everything we've been waiting for, genuinely."
Fr Kelley, who comes from Ireland, will return to the ITV talent show after learning he has progressed to the next stage of the competition.
Speaking to camera crews backstage a short time after his performance, he said: "I just had the most amazing experience on the stage singing 'Everybody Hurts'.
"The four judges gave me a standing ovation; I mean, come on, it doesn't get better than that.
"I'm shaking still; I'm absolutely shaking because I genuinely, genuinely wasn't expecting that at all."
The 64-year-old from Oldcastle in County Meath will be joined in the next round by a teenage survivor of last year's Manchester Arena attack.
Thirteen-year-old Hollie Booth, and her dance troupe, Rise, got the greenlight from judges after performing to a medley of tracks by Ariana Grande.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.