Playing in his first event since calling an early end to his injury-plagued and winless season in October last year, four-time major champion McIlroy came into the third round three shots behind Ryder Cup partner Pieters after following up Thursday's 69 with a sparkling 66 on Friday.
And the Northern Irishman continued to make big strides up the leaderboard on day three, carding eight birdies and a solitary bogey to get to 16-under par and close the gap to a single stroke.
After his round, McIlroy told Sky Sports Golf: "I putted really well and hit the ball very well. So all in all, it was another great round and another really good confidence builder -- not just for this week but for the rest of the season, as well."
McIlroy has an impressive record at Abu Dhabi Golf Club, with four second-placed finishes to his name and added that he would love to go one better this year.
"It would mean a lot. I've had a lot of close calls here, I think about six top threes or something like that. I've never won my first start back out. I was close last year in South Africa, Stormy [Graeme Storm] beat me in a playoff. I'm excited to get back on the horse and give myself another chance tomorrow."
After firing five birdies and no bogeys in his first 17 holes, Pieters produced a good par save at the last to remain at the summit and Fisher joined the Belgian on 17 under after closing his 7-under-par 65 with a birdie at the 18th.
Fitzpatrick produced the lowest round of the day, carding 10 birdies and one bogey in his superb 63.