McDowell added a flawless 67 to his opening 66 for an 11-under-par halfway total in the £5.8million event on the Blue Monster at Doral, finishing one shot ahead of Phil Mickelson after the left-hander returned a second straight 67.
But Woods was looking in ominously good form as he sought a seventh win in the event and a 17th WGC title of his career.
The former world No 1, joint- leader overnight after a 66 on Thursday, opened with three pars before picking up shots at the fourth and fifth from close range. Another birdie from seven feet on the seventh took him into the outright lead for the first time, while a wayward drive on the par-five eighth could not prevent another birdie after he pitched to 15ft and coaxed in a curling putt.
Out in 32, Woods also birdied the tenth, 11th and 13th and was briefly three clear of the field until McDowell – who had started on the back nine – birdied the eighth and ninth to set the clubhouse target, while Mickelson almost holed in one on the ninth to also finish his round in style.
McDowell told Sky Sports: “It looks like Tiger has got the eye in round here and he is always exciting when he is playing well. But I am very happy with my performance over the first two days. I’m feeling really good on these greens and positioned it well off the tee which you have to do on the course.
“I saw Phil (Mickelson) on the board and the possibility of the dream pairing of Phil and Tiger tomorrow, and I said to my caddie, ‘Let’s try and spoil that party’.If I can be hanging around come Sunday afternoon on the back nine and give myself a chance, that would be nice.”
McIlroy had at least got himself into red figures, but at one under par with five holes to play was 12 behind playing partner Woods. The 23-year-old has dominated the golfing headlines this year, firstly for signing a multi-million pound deal with Nike and then missing the cut in his first event with his new equipment in Abu Dhabi.
He then lost to Shane Lowry in the first round of the WGC Accenture Match Play, before things went from bad to worse as he quit the defence of his Honda Classic title last week after completing just eight holes of his second round.
McIlroy issued a full apology for his withdrawal on Wednesday, admitting the pain from a wisdom tooth and being in a “bad place mentally” was no excuse for walking off the course after playing those eight holes in seven over par. However, a full weekend working with coach Michael Bannon on a swing flaw had not done the trick, with the Northern Irishman admitting there was no quick fix at hand before shooting an opening 73.
A two-putt birdie on the first today was the ideal start, but McIlroy bogeyed the fourth and sixth before a birdie on the eighth took him out in 36. Birdies on the 10th and 12th showed glimpses of his talent, but he was also getting a close-up look at a rejuvenated Woods.
Scott Jamieson was four-under for the event with two to play but Stephen Gallacher and Paul Lawrie were both down near the foot of the field.