McIlroy reached the event's halfway stage 11 under at 133, having done most of the hard work a day earlier with a first-round 63.
He is one shot ahead of the United States' Brooks Koepka, who followed his first-day 69 with a 65.
Scoring on Friday proved tougher for most players as Thursday's lush greens dried out under the unforgiving Gulf sun, with the Northern Irishman's playing partners Woods and Stephen Gallacher shooting 73 and 71 respectively.
That left Woods on 141 and defending Dubai champion Gallacher on 137 and outsiders for the $417,000 first prize.
McIlroy, whose last tour victory was at 2012's DP World Tour Championship also in Dubai, began inauspiciously, pulling his opening drive into the rough and then fluffing a 12-feet par putt for his first bogey of the tournament.
The world number six's tee shots were also wayward on the next two holes, but a sumptuous bunker shot allowed him to sink a three-foot birdie putt at the third.
The 24-year-old picked up another shot on the fifth as he made his first fairway of the round and reasserted his grip on the tournament with a five-foot birdie at the seventh and another at the 10th.
Two bogeys at 13 and 16 threatened to pull the former U.S. Open champion back into the pack, but a birdie on the last gave him some narrow breathing space going into Saturday's third round.
Woods rarely sparkled, hitting the fairway on only four occasions and failing to take the more difficult birdie opportunities he would have sunk in his pomp, although he did end a run of 11 successive pars with a birdie at the third.
A scuffed seven-footer at the sixth and another fluffed putt at the ninth led the 14-times Major winner to drop two shots and he did little on the back nine, whose three par-fives and two par-threes usually offer more opportunities to pick up shots.
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- Stephen Gallacher