Northern Ireland's US Open champion, who refused to speak about his management switch after his opening 64, added a 69 to be 11 under par and two in front of 20-year-old Korean Noh seung-yul.
McIlroy was overtaken when he double-bogeyed the ninth, but collected birdies at the 11th, 13th, 15th and 18th.
Noh's 63 swept him one ahead of third-placed pair Louis Oosthuizen and Anthony Kim, while Padraig Harrington is tied fifth with Hunter Mahan and joint seventh are Ian Poulter and Robert Karlsson.
Lee Westwood's 70 left him six behind with Charl Schwartzel, Colin Montgomerie and John Daly.
McIlroy, in the water for his double bogey, stated: "I had a good back nine - to shoot four birdies kept me going and I will try hard to keep hitting the birdies needed to win this weekend."
Noh, having taken the day-old course record set by McIlroy, said: "I have hurt my ankle and have not been able to practice too much or swing as hard as I would like.
"I just decided to be careful, putted well and chose good options."