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 he would love to go one better this year.
He added: "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 play-off.
"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 seven-under-par 65 with a birdie at the 18th.
Defending champion Tommy Fleetwood and fellow Englishman Matthew Fitzpatrick were in a tie for fourth place on 15 under.
Fitzpatrick produced the lowest round of the day, carding 10 birdies and one bogey in his superb 63.
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