Fleetwood is 15-under overall after he shot the lowest round of the day, and after starting out three shots off McIlroy, by the sixth hole he had already overtaken his Ryder Cup teammate.
"I played very well, got off to the perfect start and was able to build some momentum," Fleetwood told Sky Sports.
"I read the greens well, got that confidence going, that rhythm and that flow. You pick up that confidence when you start holing a few putts."
The Englishman hit four early birdies while world number two McIlroy's bogey on the fifth cancelled out his birdie on the previous hole, and the battle continued on the back nine with both players hitting three consecutive birdies.
Fleetwood had extended his lead thanks to a birdie on the 10th, but McIlroy pulled the gap back to one shot when he birdied the 16th to set up an exciting final round at the inaugural Dubai Invitational where the winner will take home $425,000.
"I'm definitely well in it. I felt I did OK, had a bit of a slow start but got things going on the back nine to try and keep up with Tommy," McIlroy said.
Thorbjorn Olesen was the only other player able to keep pace, and the Dane remains three shots off the lead after carding a five-under-par 66.
