McIlroy remains world number one after beating bitter rival Reed in Dubai
It was the first time McIlroy has won the first start of his new season and is his 15th DP World Tour victory in 231 starts.
His one-stroke victory was also his third Dubai Desert Classic success in 13 appearances.
He will remain world number one, after Spaniard Jon Rahm failed to win the Farmers Insurance Open on the PGA Tour on Saturday.
McIlroy and Reed went into the tournament after a row when Reed reportedly threw a tee towards McIlroy on the practice range in Dubai.
The incident, caught on camera, turned out to be a lot milder than reported but the two have been at odds since McIlroy criticised players, including Reed, who joined the rival Saudi-backed LIV Golf circuit.
Relations were not helped by McIlroy receiving a subpoena from Reed's lawyer on Christmas Eve to appear as a witness in a case.
McIlroy had fallen behind Reed after a bogey on the 15th hole but he made amends with birdies on the 17th and 18th in a round of four-under par 68.
The Northern Irishman finished on 19-under par, while Reed, starting the day four shots behind McIlroy, made a crucial bogey on the 16th and a par on the drivable par-4 17th hole in his round of 65.
"I think, mentally, today was probably one of the toughest rounds I've ever had to play because it would be really easy to let your emotions get in the way," said McIlroy, who won $1.53 million (£1.23m) for his effort.
"I just had to really concentrate on focusing on myself. I had to forget who was up there on the leaderboard, and I did that really well."
McIlroy blew his chances last year when he hit his second shot into the water on the final hole - and he almost repeated the scenario with his tee shot on the 18th.
"Honestly, I feel I got lucky that my ball didn't go in the water. It's such an awkward tee shot for me," he said.
"Driver is too much and 3-wood is not quite enough. So I tried to hit a sort of easy driver and it came out really, really hot. I needed to lay up and try to get up-and-down that way.
"I said, 'fool me once and fool me twice', but I wasn't going to get fooled a third time. It was nice to be able to play the percentages and make it pay off."
'Hats off' to McIlroy
McIlroy said such an early first win was even sweeter as he was not playing his best golf through the week.
"It means a lot. It was a battle all day. Honestly, it's been a battle all week," said McIlroy.
"I really feel like I haven't had my best all week, but I just managed my game so well and played really smart."
Reed edged ahead by a shot when McIlroy made a bogey on the par-3 15th but gave it up on the next hole when his drive got stymied by a tree.
He then had to take a drop shot on the 17th from a small bush, and could not take advantage of the drivable par-4.
"I'm happy with that finish. I felt like we were probably almost playing for second going into the day," said Reed.
"I knew what I had to do early. I went out there and I put the pressure on him. You know, being four back of a guy like Rory is not easy.
"Hats off to him, he played some great golf."
Australian Lucas Herbert, champion in 2019, closed with a six-under par 66 to take solo third place at 16-under par 272.
England's Callum Shinkwin, who started with three bogies in his first six holes playing in the lead group with McIlroy, made six birdies after that to shoot a 69 and take solo fourth place at 273.
The DP World Tour stays in the United Arab Emirates for a fourth consecutive week and will head to the northern emirate of Ras Al Khaimah this week for the $2 million RAK Championship.
