Amid scenes reminiscent of his halcyon days, Woods brilliantly birdied six of the first seven holes after starting the day tied for the halfway lead with world No 1 Rose at East Lake.
The 14-time major champion cooled off on the back nine but a five-under-par 65 put him in prime position to record his first victory since 2013.
Woods posted a 12-under 198 total while Englishman Rose recovered from a bogey, bogey start to card 68.
Northern Irishman McIlroy birdied the par-five 18th for a 66 that earned him a date with Woods in the final pairing for Sunday's last round.
Woods has 79 PGA Tour victories, three short of the record held by Sam Snead.