The British world number nine, who missed the cut in last week's Players' Championship on his first appearance since winning the year's first major, dropped only one shot at the K-Club on the outskirts of Dublin.
Four-times major champion McIlroy, the world number three, birdied the 18th at his home Open to complete a round of 67, one shot ahead of young Briton Callum Shinkwin and South African Jaco van Zyl.
Dubai Duty Free Irish Open
Willett, Warren lead Irish Open, McIlroy one shot back
20/05/2016 AT 18:07
The 28-year-old Willett's round of 65 was only one shot off the course record set by South African Charl Schwartzel in 2003.
Golf
Hero World Challenge tee times, TV Coverage, prize money as Hovland defends in Tiger's tournament
15 HOURS AGO
Hero Open
Woods withdraws from Hero World Challenge with foot injury
YESTERDAY AT 20:02