McIlroy carded a 75 for a six-over total of 150 while playing partner Woods was given a belated two-shot penalty for an incident at the fifth hole and missed out as well after having to sign for a 75, rather than a 73, for a tally of 147.
Woods faced an anxious wait before the two-over-par projected cut of 146 was confirmed to send him home, with Justin Rose leading at the half-way stage after rounds of 67 and 69.
McIlroy made an inauspicious start to his Nike career, and there was certainly no tick against his scorecard as, playing with new clubs and a new ball, he swished and swooshed his way to a second successive three-over 75 in his first competitive outing since signing a massive sponsorship deal with the US sportswear firm on Monday.
McIlroy followed a run of three straight pars with bogeys at the fourth, fifth and seventh before birdies at the eighth and ninth offered some hope that he might squeeze into the final two rounds on Saturday and Sunday.
However, the 23-year-old looked a picture of despair after dropping more shots at the 10th and 14th to post a six-over total of 150 in the European Tour event at the Abu Dhabi Golf Club.
"It was pretty much the same as yesterday," McIlroy said. "When you don't hit the fairways on this course you can't score.
"I didn't drive the ball well, I didn't putt well again and my iron play wasn't anywhere near the standard that is usual for me. All aspects of my game were off.
"I'm also struggling with my swing a little bit. I feel like I'm spinning out of it a lot, hitting off the heel. I just need to put in a bit of work on the range," said McIlroy.
"I knew it was going to be a tough week with everything that's been going on. I was looking forward to getting back to the course and doing what I'm comfortable with - it just didn't work out like that."
Twice major winner McIlroy said he would stay in Abu Dhabi over the weekend to work on his game.
"It's the first week," he said, referring to his new clubs, "so I wouldn't read too much into it. If anything it's more the Indian and the arrow at this point.
"I'll work on the range for a few hours tomorrow and try to clear a few things up with my coach."
McIlroy temporarily ditched his new putter on Friday after having struggled with it in the opening round.
"I just felt the greens I've been practising on in Florida are a lot faster than these ones here," he said. "The Nike putter is great on those.
"Here it's a weight issue more than anything. I could feel the head of this heavier one I used today is a little better but even when I got the ball to the hole it didn't go in so it was to no avail."
McIlroy will now take a four-week break from competitive golf before reappearing at the WGC-Accenture World Match Championship in Arizona.
14-times major winner Woods, meanwhile, made a dreadful start, dropping strokes at three of the first four holes before making another bogey at the fifth.
Six holes later tournament referee Andy McFee informed Woods he might have to sign for a triple-bogey seven rather than a bogey five.
Woods had struck a wayward shot into a desert bush at the fifth and, after consulting playing partner Martin Kaymer, the pair agreed he should be allowed a free drop because it had become imbedded.
The regulations, however, only allow for a free drop in such circumstances if the ball has finished anywhere but in sand and Woods was therefore handed his penalty at the end of the round.
"It's tough because I didn't get off to a good start but I fought and got it back," the 37-year-old American told reporters after eventually posting a three-over-par 75 for a three-over tally of 147.
"I was right there and I felt if I was even-par overall I had a chance going into the weekend, being only eight back of the leader (Britain's Justin Rose). Evidently it wasn't enough."
Woods had produced a scorching run of five birdies in nine holes from the eighth, including three in a row to the 16th, but his valiant effort proved in vain.
Kaymer said he and Woods were unaware of the distinction in the rule between grass and sand.
"The referee came up to us on the 11th hole and said the sand area was not like normal grass so he was apparently not allowed a free drop," said the German after shooting a 69 for 140, four under.
"I didn't know about it and he obviously didn't know about it otherwise he wouldn't have done it. It's an unfortunate thing."
McFee said he spoke to Woods at the 11th because he was aware of his position score-wise.
"Once we had established what had gone on...I had a conversation with Tiger," he explained. "I wanted him to know there was a possibility a penalty had occurred.
"I thought he might want to have a look at the exact spot, take me there and say 'well, that's where it was'.
"In the end Tiger wanted to discuss it in the recording area rather than the golf course," added McFee. "There we had further discussions and he was happy to accept it.
"He said, 'If you think that area is not entitled to a free drop, that's good enough for me'. It was just one of those situations where he and Martin got the rule wrong."
McFee said he was alerted to the incident at the fifth hole by one of his referees.
"Spectators out on the course spoke to a referee," he explained. "They were curious why the drop was given.
"I don't think they realised the issue they were starting. The referee went to the area...and then called me. I went to look at it and for sure there is no question the ball was imbedded in sand," added McFee.
"We've had a number of rulings here in Abu Dhabi and in Dubai where players have asked for relief and been denied. It happens all the time."
Woods said his general play was not up to scratch in the first two rounds at the fiendishly difficult Abu Dhabi Golf Club.
"I didn't hit it particularly well," he added. "I putted great but I just didn't hit it very good - I was struggling with that.
"I have some work to do and next week I'm playing at Torrey Pines (at the Farmers Insurance Open in California) so I'm going to go back and get ready."
- Sports & Recreation