Ilonen had a 3-under 68 to reach 10 under. He opened with a course-record 64 on Thursday.
The 34-year-old Finn birdied his opening hole, followed with eight straight pars, then had four birdies and two bogeys on the back nine.
''I wanted to at least get to 10-under par and I did that,'' Ilonen said. ''It wasn't as easy today and I didn't hit the ball that well but I putted well and it was good enough.''
The loss of McIlroy, from Northern Ireland, was a blow to event organizers. He followed his opening 74 with a 69 to miss the cut for the second straight year in the national open.
McIlroy had a double bogey on par-5 fourth after his tee shot clipped a tree and ricocheted out of bounds and over the fence into the adjoining Fota Island Wildlife Park.
''I'll be back next year and try and do better,'' McIlroy said.