Fleetwood, who celebrated his 27th birthday on Friday, started the day two behind joint-leaders Fisher and Thomas Pieters and made a solid start with back-to-back birdies at the second and third.
That inspired back-nine run was key to Fleetwood's success, with a sequence of five birdies in seven holes from the 10th proving more than McIlroy could handle.
Rory McIlroy may have been something of a forgotten man during his injury-riddled 2017 season, but the fit and self-assured golfer who kicked off his 2018 season with a robust T3 finish in the Middle East has a message for his peers: I'm back, baby. I just really wanted to win this one", said Fleetwood, who is expected to advance from 18th to 11th in the rankings on Monday."I had the year of my life last year. His own report was telling: "Without the wind I played good and in the wind I didn't play that good". "I feel a lot more emotional, actually, than previous year". "To put that round of golf together out there today; 65 in those conditions is seriously impressive and six under on the back nine when he needed to".
McIlroy now is focussed on more tournament play ahead of the eight tournaments scheduled before attempting to complete the career grand slam with victory in the Masters. But, yeah, I couldn't really make a putt. My game was probably better than I expected it to be. "After so long away, I didn't really know what my expectations were coming in. I was just in the moment and seeing the shots". Just backing it up is the next big thing really, to keep going and hit form early. "It's a very, very nice feeling".
"If I can play the same way I played this week, I'll have a good chance again next week".
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Irishman McIlroy, playing in his first event since October, shot up the leaderboard into third spot with a couple of late birdies for a 65 to stay in the hunt at the Abu Dhabi Golf Club.
"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", said McIlroy, who last won at the TOUR Championship in Atlanta in September, 2016.
He said: "Hats off to Tommy".
Fleetwood excelled in hard conditions, carding six birdies over the closing nine holes and drew praise from McIlroy, who simply said: "That was obscene". I felt like shooting anything in the 60s would have been a good score.