Harding hit a bogey on the eighth hole but recovered with two birdies on the 12th and 13th to finish at 12 under.
“I thought I played quite solid. It was a difficult day, to be fair, some tough flags to get at,” said Harding, a 35-year-old who has won two titles on the European Tour.
“There were times when I didn’t quite put the ball in play and I couldn’t really go anywhere near them.”
McIlroy, who had an eventful performance with three bogeys, four birdies and an eagle, said it was “a bit of battling” amid tricky conditions at the Emirates Golf Club.
“I think it was a fair reflection how I played,” the player from Northern Ireland said. “Some good things in there and a couple bad things as well.
“I feel like it all evened out by the end, and it was nice to birdie the last and shoot something in the 60s and play myself into the final group tomorrow.”