They will be hoping for a better showing than a year ago when both opted to start their season in nearby Abu Dhabi and, playing together, miserably missed the cut.
This time, both players have already lit the fuse to their new seasons with contrasting fortunes.
The 38-year-old Woods missed a Saturday, third round cut at Torrey Pines after matching his worst-ever score on US soil, a seven-over 79 for the most inauspicious of starts.
He made no comment afterwards other than a – “No I’m done” – when asked to comment on his round.
Of course Woods has rebounded from a poor showing in double-quick time before, notably last year when he went straight from Abu Dhabi to win the Farmers Insurance Open at Torrey Pines – the first of five titles in the year en route to another Player of the Year award.
In contrast, McIlroy came within a two-stroke rules violation of winning in Abu Dhabi which would have seen him take back-to-back titles following his victory in the Australian Open late last year.
He believes all is in place for him to produce another stellar year, rebounding from his travails of 2013 when an equipment change and business-related distractions left him befuddled.
“I have started off the year well,” McIlroy said.
“I was a little disappointed coming off the second place in Abu Dhabi. I felt like I should have won but there were a lot of positives to take from the week. I played very well.
“I felt like I could have done a few things better which I have worked on over the last week to go into this tournament in Dubai but all in all I am in a good place and really looking forward to 2014.”
What is sure is that he will be wary of the wounded Tiger, missed cut or no missed cut.
The two biggest names in golf have played together in tournaments several times but never down the home stretch in a major and they have yet to produce fireworks when in the same grouping.
“It’s great to have him here [in Dubai],” said McIlroy of Woods’ return to the bustling emirate after a two-year absence.
“He got off to a bit of a slow start to the season so he will be wanting to make up for that this week. I think he has still got a few good years left so I am looking forward to battling with him down the stretch a few times.”
Joining Woods and McIlroy will be defending champion Stephen Gallacher of Scotland, who is desparate to stash up some big Ryder Cup points to give himself a chance of making the European team for the showdown with the United States on home turf at Gleneagles in September.
In the strongest European Tour field of the season so far, world number three Henrik Stenson of Sweden, the 2007 champion, will be one to watch along with record three-time former winner Ernie Els, in-form Jamie Donaldson of Wales and 2012 champion Rafael Cabrera-Bello of Spain.