McIlroy, who finished second at the UAE capital's tournament in three of the past four years, ended the day level with playing partner Rickie Fowler who was making his Middle East debut.
Despite a first-hole birdie McIlroy, 25, struggled for rhythm on the season opener for many of the European Tour's prominent players, finding sand as a bogey at his eighth hole left him on par at the turn.
Fowler, a year older than the Northern Irishman, acted as pace-setter with birdies at his sixth and eighth holes and another at 10 to move three stokes clear of McIlroy.
The world number one's body language, hands on hips and head down after missing a birdie chance on the same hole, betrayed his frustrations as he struggled to spark his game into life.
"He (Fowler) was kicking me on today," McIlroy told reporters. "I didn't want to let him get too far ahead. It looked like he was going to shoot quite a low one, I was in neutral and needed to get something going."
That moment came at his 12th after he drove his ball to the bunker edge for a tricky second shot to the green, but a precision wedge while straddling the sand gave him a 12-foot birdie putt he duly converted.
"I was just trying to get it anywhere on the green," said McIrloy. "It's not something you ever practise, it's all feel and instinct. It was the first one I saw go in for a while so it got me going and gave me a bit of confidence on the greens."
Emboldened, the four-time major winner picked up four more shots in the next five holes, all by sinking putts from 10 feet or more as midday approached.
McIlroy's surge reeled in Fowler, despite the world number 10 making four birdies on the back nine, and a bogey at the last left them level.
They trail Kaymer (64), Belgium's Thomas Pieters (65) and five players on 66 including Briton Tyrrell Hatton and French duo Gregory Bourdy and Alexander Levy.
U.S. Open champion Kaymer – a three-time Abu Dhabi winner - was one the few late starters to thrive on a sweltering, blustery afternoon, sinking 10 birdies.
"I putted well," the German told reporters. "I hit a lot of fairways, my irons were quite sharp. It's very difficult to shoot a bad score when you play like this."
(Reporting by Matt Smith; editing by Martyn Herman)
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