Spieth held a five-shot overnight lead on nearest challenger journeyman Charley Hoffman with the rest of the field lagging seven or more strokes back.
The icy cool 21-year-old American has threatened to turn the year's first major into a runaway as he reached the halfway mark in a Masters record 36-hole total of 14-under 130.
But Woods, a four-time Masters champion, was mounting one of his patented third-round charges with a run of three birdies from the second to race up the leaderboard.
With soft conditions, the early starters were able to attack the most difficult pin positions of the week, 2011 Masters champion Charl Schwartzel of South Africa and 2013 winner Adam Scott of Australia getting in on the chase with birdies at the second and third to join Woods on five-under.
World number one Rory McIlroy, bidding for a career grand slam, made a spectacular start with an eagle on the par-five second to fly up the leaderboard and join a large group on four-under.
McIlroy, who was on the brink of missing the cut with nine holes to play on Friday, and twice defending champion Bubba Watson were one of the several marquee pairings attracting large galleries on another muggy afternoon at Augusta National.
Woods and Sergio Garcia are another pairing in the spotlight, the 14-time major winner and the fiery Spaniard having engaged in a long-running feud. – Reuters
Original source: Woods on the charge at Augusta