The world No 1 picked up his first shot at the 10th – his opening hole – but dropped back to level par before coming into his own with a hat-trick of birdies just after the turn.
Another birdie, after a superb putt at the seventh, lifted the Northern Irishman to four-under after 16 holes.
At that stage Fowler was two shots ahead, sharing the lead, but the American bogeyed his final hole while McIlroy rattled in another birdie on his penultimate hole for his 67.
On a crisp morning in the United Arab Emirates, McIlroy’s sumptuous chip to 10ft on his opening hole had given him the chance to begin the season with a birdie, and he did not pass it up.
That failed to inspire him though, and he struggled to create many birdie chances before eventually bogeying the 17th after a wayward 8ft putt.
The 25-year-old appeared in trouble on the third, his 13th hole of the day, after his tee shot left him on the lip of a bunker but he superbly managed to get his approach shot onto the green before holing for birdie.
Two more birdies followed and he then holed a 15ft putt on the seventh to leave himself in a decent position before his final birdie at the next and a par to finish.
McIlroy said: “I was just trying to keep up with this guy (Fowler). He was making birdies. I hung around in the middle of the round.
“It was a nice finish and I’ll need to do more of that in the next few days if I’m to have a chance to win. I’ll need to hit more fairways as well. I didn’t drive the ball particularly well today.
“I need to do a little bit better if I’m (going) to have a chance.”
Fowler enjoyed birdies at the 15th, 17th, first, fourth, fifth and seventh to head the leaderboard before his only mistake at the ninth, his final hole, saw him slip back to join McIlroy on five-under.
England’s Tom Lewis illuminated his round by enjoying a hole in one on the par-three 200-yard seventh for the 10th ace in tournament history and third on that hole. He finished on three-under, four behind early pacesetter Thomas Pieters of South Africa.
Pieters, who has never won on the European Tour, claimed the outright lead??after recovering nicely to birdie the 18th.