Two-time Abu Dhabi winner Fleetwood put himself in contention with a 71 despite struggling with his putter.
Sweden’s Sebastian Soberberg and Denmark’s Thorbjoern Olesen are also on 15 under, while Lowry followed up an eagle at the par-five second with five birdies in a round of 66.
Belgian Thomas Detry carded a 10-under bogey-free round of 62 to join a group of six players on 14 under which also includes Scotland’s Robert MacIntyre and England’s Tyrrell Hatton.
Northern Ireland’s McIlroy, who started the day nine shots off the lead, cut that gap to three before falling back with a seven at the last. His 69 left him 13 under.
He will win the Race to Dubai for a sixth time if he finishes in the top two in Abu Dhabi, before the European Tour season finale in Dubai next week.
“I sort of dug myself a bit of a hole to get out of, but I can still go into tomorrow feeling like I have half a chance,” said McIlroy.
“I bogeyed the first today and doubled the last, but in between that I played some really good golf. I just need to keep the big mistakes and big numbers off my card.”