Woods, beaten 2&1 by fellow- American Charles Howell in a first round still to be completed following Wednesday's snow, has the comfort of knowing he has already won a title this year.
But world No.1 McIlroy, who lost on the final green to 68th-ranked fellow-Irishman Shane Lowry, will know there are more questions coming after what has to go down as a shocking start to the season.
The 23-year-old exited last night after an approximate four-over-par 76. Next week he defends the Honda Classic in Florida.
"I drove really well, but couldn't take advantage of that," McIlroy said. "If I'd hit my irons better it could have been a different story.
"I could have been three or four up early on, but let Shane get back into the match and he had a nice little run."
Dubai Desert Classic winner Stephen Gallacher lost 2&1 to 2010 winner Ian Poulter, Paul Lawrie found American Scott Piercy too hot to handle and lost 4&3, then Richie Ramsay could not hold on to a two-hole after 11 playing fourth seed Louis Oosthuizen. The South African won on the 17th.