The Northern Irishman had slipped off the top of the pile on Friday following a disastrous second round in which he landed in the water four times.
But the world number two course-corrected in the third round as he brought his score to five-under.
"A little better than yesterday, kept the ball dry instead of the four water balls I had," McIlroy said.
"It was a tricky enough day, got off to a bit of a slow start, but stayed patient and hung in there and was rewarded with birdies on the back nine."
Despite holing three birdies on his way back to the clubhouse, McIlroy still remains three shots back on leader Nacho Elvira after the Spaniard carded another impressive round to go out on his own at the top of the pile.
Tied overnight with Republic of Ireland's Shane Lowry, Elvira now holds a two-shot lead following back-to-back 68s after the 2019 Open Championship winner dropped to joint-second with England's Marcus Armitage and South African Dylan Frittelli on six-under.
"I've been here long enough to not be too nervous tomorrow, let's put it that way," 38-year-old Elvira said.
"I think I'm going to try to enjoy and probably learn from all the experiences that I have in the past and see where that puts me."