She dedicated the first song to Prince, who famously wrote Nothing Compares 2 U before O'Connor enjoyed worldwide success with it in 1990.
The singer appeared dressed in a traditional Muslim hijab and discussed her conversion to Islam late last year, which was around the time she changed her name to Shuhada Sadaqat.
Two days after her performance she also apologised for previous social media remarks in which she labelled white people "disgusting".
Writing on Twitter, she explained she had been "angry and unwell" when she first made the "crazy tweets".
"As regards to remarks I made while angry and unwell, about white people... they were not true at the time and they are not true now," she wrote.
"I was triggered as a result of islamophobia dumped on me. I apologize for hurt caused. That was one of many crazy tweets lord knows."
The apology and her live television appearance came ahead of her first Irish tour in five years.