Woods, who posted his best round in two years on Thursday with a six-under-par 64, backed it up with another solid round to card a 65 and join Tom Hoge on 11 under at the top of the leaderboard.
The 14-time Major champion might even have taken sole possession of the lead had it not been for an uneven front nine, which comprised two bogeys and three birdies to put Woods one under for the day at the turn.
It got better on the par-five 15th, however.
A sensational second shot took Woods over the water and onto the green in two, 10 feet from the pin.
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The former world number one duly rolled in the putt for an eagle which took him to 11 under before he closed out the round with three straight pars.
The round leaves Woods perfectly poised to achieve what had seemed an improbable goal before the tournament -- a victory which would guarantee him a berth in the lucrative four-leg post-season.
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It comes after a disappointing display at the PGA Championship at Whistling Straits last week where he missed the cut -- his third missed cut at a Major this year.