The four-time winner edged his opponent 25-22.
He came up with a cracking bowl to clinch the win. He was potentially trailing the head by one shot but drew the shot with a toucher with his last bowl.
Earlier in the game it appeared as if he might not have to work so hard. He was up 15-3 after about an hour. But Wheeler found his range and clawed his way back into the match.
"Regardless of who you play you should always expect a momentum swing at some point and I was just fortunate at the start that he was still searching," McIlroy said.
"That allowed me to get a bit of a lead. But then there was just a subtle change in the line to the jack.
"It got a bit wider and wider to where he was playing initially.
"They started landing on the jack and he got a lot of first bowls close. That’s the key to singles."
Wheeler also saved the game twice with his last bowl and proved a tenacious opening opponent.
It was perfect preparation for the rest of the tournament which concludes on Monday.
McIlroy is the only player to have won the tournament four times.
"The closer the games the better. If you are put under pressure in your section it leads on to good form if you are able to scrape through.
"Being tested early doors is actually a really good thing."
McIlroy won the 30-year-old tournament at his first attempt as a teenager in 2006. The 2018 World Singles Champion of Champions has entered each tournament since with a target on his back.
"Outside of the national singles it is the premier event in the country and one that the guys really look to do well in.
"You only have to look at the guys who have won this event."
Previous winners include the likes of Ali Forsyth, Rowan Brassey and Mike Kernaghan, so it is a real who’s who.
McIlroy used to feel the pressure earlier in his career but these days he is more relaxed.
He has mostly done well at the event and enjoys returning year after year.
He has noted a "bit of a demographic change" this year, though.
"It used to be all the old dogs and I used to be the kid," the 33-year-old said.
"But now I feel like one of the older ones and there are all these young fellows and I need to prove my worth before they take over."
