Ilonen birdied five of his closing seven holes in superb scoring conditions to end the day with a two-shot lead on the Fota Island course.
Ilonen had just 26 putts on the occasion of his 300th European Tour event. It added up to a record on a course made over since the last Irish Open at Fota Island in 2002.
The Finn, a three-time winner on tour, wasn't surprised at the fifth course record in his career.
"I lost out in a playoff to Sergio (Garcia) in the Qatar Masters this year, and recently in the Nordea Masters I felt my game was good despite finishing 32nd, which is still a mystery how I finished 32nd that week as I was hitting my best shots of the week there," Ilonen said. "Maybe the good golf is there but then we still have a long way to go."
McIlroy hit just eight of the 14 fairways and took 30 putts in a round of 3-over 74. He's in a lowly share of 125th place in the 156-player field.
"I've still got a little bit of jet lag, for sure, coming from the U.S. Open," he said. "I wasn't able to do much the Monday, Tuesday, because the clubs didn't arrive until yesterday, as well, so that was a little bit frustrating more than anything else.
"But I did a really good practice session on the range last night after the pro-am, and was feeling good going out this morning. However, I just couldn't really put it together as I was very sloppy with the scoring clubs, wedges, the short game, the putting. All that was just a little off.
"Hopefully, that is my poor round for the week."