Among the home players, Cam Smith had a wobbly start with a bogey on the sixth hole, but the 2022 British Open champion responded well in the latter half, with an eagle on the 14th hole to card a 66.
The 32-year-old was in front through the 17th, before getting a bogey on the last hole, while Neergaard-Petersen grabbed three straight birdies to overtake him by two shots at 14-under overall.
“I didn’t feel like I had my best stuff out there today and didn’t feel as comfortable over the ball,” Smith, who sits joint-second with Mexico's Carlos Ortiz and South Korea's Si Woo Kim, told broadcasters.
“But I just went through the process, hit the right shots and didn’t shy away. I’m happy I did that, it was what I was most impressed with.”
Banana skin
The five-time major champion McIlroy had another nervy start with a double bogey on the second hole after his tee shot settled on a banana peel in the rough, forcing him to play it as it lay to avoid moving the ball and incurring a penalty.
But the Northern Irishman bounced back quickly, and once again finished strong to card a 68. He will start the final day at five under, nine strokes off the leader.
“I didn’t get off to the greatest of starts but I felt I responded well,” McIlroy said.
“I’ll probably be a little too far behind to try to challenge on Sunday but I will try to end the week on a positive note and shoot my lowest score.”