After a near two-hour thunderstorm delay Woods eagled the third and birdied the fifth, seventh and 11th holes to charge from 18th place to joint fourth.
He was still four behind McIlroy, however, after the 22-year-old Northern Irishman parred the opening seven holes to remain 11 under par.
McIlroy, who has to win to end Luke Donald's nine-month reign as world number one, was having to work hard.
He sank par putts of 13 and eight feet on the second and fifth, then a 15-footer at the short seventh, but his overnight two-stroke lead was down to one as 43-year-old American Tom Gillis covered the opening stretch in one under.
England's Justin Rose was not out of it. After a 27-foot birdie putt on the first he bogeyed the next, but then holed from 50 feet at the seventh and on eight under was in outright third place.
Woods also sank a 27-footer for his eagle and then added putts from nine, 10 and 14 feet - and almost made one of nearly 60 feet on the 10th.
World number three Lee Westwood matched Woods's outward 31 and when he almost pitched in at the 13th he was up from 18th to seventh on six under.