World No. 3 McIlroy may have had his problems on the tee but on the green he devoured most of the birdie chances that came his way to join Swede Robert Karlsson in the early lead on five-under-par 67.
The 22-year-old Briton began his round at the 10th and quickly left world No. 1 Donald (71) and 14-times major winner Woods (70) trailing in his wake by grabbing a hat-trick of birdies from the 11th.
McIlroy's charge slowed when he bogeyed the 14th and 17th but four birdies in the closing 10 holes put the smile back on his fresh-faced features.
"The club is coming down to the ball differently to the way it normally does for me so I'm just finding it difficult to trust myself to release the driver.
"That's something I'm going to have to work on this afternoon on the practice range. I'm going to need to hit the ball in the fairway a lot more tomorrow and over the next three days."
McIlroy has finished fifth, third and third here in his last three visits and is hoping to break Martin Kaymer's winning sequence, the German having lifted the prized Falcon Trophy in 2008, 2010 and 2011.
"I feel like this course suits me really well," said the Northern Irishman. "There's just one problem - it suits Martin Kaymer even better."
Woods, making his Abu Dhabi debut and like his playing partners competing in his first tournament of the season, was in ominously good form from tee to green.
The former world No. 1 struck the ball supremely well, reeling off 16 pars and two birdies, the only thing missing was a hot putter.
"I controlled my ball all day and just had a hard time getting a feel for these greens," said the 25th-ranked Woods.
"I didn't quite read them and my speeds went off because I just didn't have it right."
Woods returned an early birdie at the 11th and should have claimed another at the par-five 18th but three-putted after missing from three feet.
The 36-year-old American almost had a hole-in-one after a majestic tee shot at the short fourth where he notched his second birdie.
However, Woods erupted in angry frustration on the eighth, smashing his club into the turf in fury after fluffing an easy-looking pitch to the green.
"You have to drive the ball well here," he said. "Rory didn't drive it that well today but he sure chipped and putted well.
"The rough is long. Sometimes you can still get the ball to the green but other times you have to just wedge it out - it's a pretty good test."
Woods, beset by injuries and personal problems in recent years, is anticipating a full playing schedule in 2012 for the first time in several seasons.
"I'm expecting to have a nice full year," he explained. "I've not had one of those in quite a while.
"I've probably not had a healthy year for close to a decade so I'm looking forward to it."
Donald, who last month completed a unique double by winning the money lists on both sides of the Atlantic, said he thoroughly enjoyed playing alongside Woods and McIlroy.
"It was fun to be a part of that threesome because Tiger and Rory are big names in the world of sport and golf," said the 34-year-old Englishman.
"We all played pretty well today and Rory took advantage of a few more opportunities. Tiger and I didn't make too many putts but it was a solid day for all three of us."
( Editing by Alastair Himmer; To comment on this story: email@example.com)