The Englishman entered the final round with a one-shot lead but found himself one behind McIlroy at the 18th tee before the Northern Irishman hooked his tee-shot into the water.
That left the door open for Fleetwood and he rolled in a 16-foot putt on the final green for a birdie-birdie finish and a one-shot victory as McIlroy made a bogey.
Dubai-resident Fleetwood's closing 67 saw him finish at 19 under, one ahead of McIlroy – who signed for the same score – and South Africa's Thriston Lawrence.
"I'm very happy," said Fleetwood. "It was amazing winning. Like almost everybody else in the world of golf, I don't win anywhere near as much as I would like to but just that winning feeling is great.
"This is obviously where I live and have a lot of support. It's great to kick off the year with a great result and push on from here.
"I was very happy with the way I played today for the large majority of the round, felt like I didn't hole some of the putts that I wanted to. I just stayed patient and kept playing. I knew I was playing very, very well, and even the last two holes, played 17 and 18 great."
McIlroy and Fleetwood's "Fleetwood Mac" partnership claimed two points from two in the foursomes in Rome last year as Europe beat the United States 16.5-11.5 but no quarter was given on a dramatic final day in Dubai.
Fleetwood found himself three shots clear of McIlroy as he picked up shots on the third, fifth and tenth, with the four-time major champion following gains on the third and fifth with a bogey on the sixth after finding the water.
A hat-trick of McIlroy birdies from the 11th had him in a share of top spot and while he inexplicably three-putted the 14th from two feet, he hit straight back with a 20-footer on the next.
Fleetwood dropped his only shot of the day on the 16th but responded from 30 feet on the 17th, as McIlroy birdied the same hole to set up the late drama.
"I'm really happy for Tommy," said McIlroy. "He's played some incredible golf over the last year without actually getting a win. So for him to get the win here, it's great for him and it will do his confidence a world of good and hopefully he kicks on from it.
"I think first week back out, I think you're going to expect some of those sloppy mistakes and unfortunately for me those mistakes came at the wrong time today. But I'll reflect on it and learn from today and there's still a lot of good stuff in there. But just need to tidy up some of the edges and if I do that, I feel good going into next week."
Lawrence finished with a 64, while England's Jordan Smith was at 16 under, one shot clear of former Open champion Francesco Molinari.
