The home favourite was in danger of letting a promising round slip away when he dropped shots at 14th and 15th to fall back to level par.
However, the world number three finished superbly to ensure he did not suffer another sticky start on Northern Irish soil.
McIlroy was nine over for his first round the last time Royal County Down hosted the Irish Open in 2015 and he was eight-over after day one of the 2019 British Open at Portrush.
"Any time you can shoot three under around this place you have to be happy," said McIlroy.
"The conditions were pretty tough early on and then the wind seemed to settle a little bit those last few holes and it was nice to take advantage of that and play them the way I did.
"Giving those shots away on 14 and 15, to get more than both of them back on the last three holes was a great way to finish and gives me plenty of momentum going into Friday morning."
England's Todd Clements leads at five under, one shot clear of Finland's Sami Valimaki and Spaniard Alejandro del Rey.
McIlroy is in a group of five at three under, which also includes South African Thriston Lawrence, who finished fourth at the British Open in July.