The Northern Irishman would birdie the second and third holes and had eight consecutive pars thereafter.
McIlroy would then go on a charge as he birdied the 12th, 14th and 17th, before finishing the 18th with an eagle for a bogey-free round.
Belfast man Tom McKibbon would card a two-under par round of 70 as he finds himself -7 for the tournament.
However, England’s Matt Wallace birdied every hole on the back nine as a career-best round of 60 handed him a one-shot lead heading into the final day of the season-ending DP World Tour Championship.
The 32-year-old started the day seven shots off the pace but made 12 birdies including nine in row from the 10th to catapult himself to 16 under.
That handed him a one-shot advantage over countryman Tommy Fleetwood and another member of Europe’s victorious Ryder Cup team in Viktor Hovland, with the playing partners both firing rounds of 66.
Wallace’s nine-hole score of 27, 12 birdies in his round and run of nine consecutive gains all match the best all-time records on the DP World Tour but after heavy rain overnight on Friday meant players could clean and place their ball on the fairways, his round will not officially enter the record books.
He was still delighted with his efforts, however, as he looks for a fifth DP World Tour win to go with the PGA Tour title he won in the Dominican Republic in March.
“What a day, an amazing day,” he told Sky Sports Golf. “I just tried my hardest to get myself back into the tournament. I’m really happy that I’ve been able to do that. Played great.
“At the end, I didn’t even think there was a 59. Honestly I think it helped me a little bit. I just played nicely coming down the stretch, just keep getting one more if I could and I managed to do that.”
After birdies on the second, sixth and eighth, Wallace set off on his remarkable run from the 10th, making eight birdies in a row and knowing that an eagle on the last would see him card just the second 59 in DP World Tour history.
He found sand with his second on the 18th but almost holed out, leaving himself two feet to complete the birdie set on the way home.
“Kind of gutted now actually a little bit,” he added. “Great opportunity to do it. I’ve done it at Moorpark on the West Course which is only a par 68, but to do it out there would have been really special today.
“Ball in hand helps. I had a couple of good lies for up-and-down, but it was fantastic and a good effort for 59.”
A 58-foot putt for eagle on the 14th was the highlight of Fleetwood’s round which also contained six birdies and two bogeys, while Hovland was blemish-free.
“I’m very happy with the fact that you get to the final day of the year and I’m still playing well, still feel fresh and I’m still motivated and in contention,” said Fleetwood.
“I take a lot of pleasure out of that. I think it’s easy to shut off when you get so far down the season but I kind of pride myself on going all the way.
“We’ll see tomorrow. It was great today. Out there playing with one of the best golfers in the world and trying to go toe-to-toe with Viktor. Just look forward to more of it tomorrow. It’s been great so far.”