After playing the back nine of the TPC-Sawgrass course in 2-under, Garcia ripped off five birdies in a row beginning at the par-5 second.
He turned in a 7-under 65 before the afternoon winds arrived to give him a 36-hole total of 11-under 133.
Woods shot his second straight 67 in a bid to capture what would be his most significant victory since his personal life unraveled late in 2009, a year in which he won six times. He has three victories this season and has climbed back to the No. 1 spot in the world rankings, but has not won a major championship since 2008.
The Players is arguably the most important event in golf outside the four majors and it carries with it the sport's richest single-tournament prize -- a first-place check of $1.7 million.
Garcia, who led at the Masters after the opening round last month and eventually finished tied for eighth, won this tournament in 2008. Woods captured the event a dozen years ago.
First-round leader Roberto Castro followed his course record equaling 63 with a struggling 78 and he fell into a tie for 29th place. Rory McIlroy, ranked second in the world behind Woods, suffered three consecutive bogeys, shot an even-par 72 and was five shots behind Garcia along with Steve Stricker, Webb Simpson and Jason Dufner.
It took a score of even-par 144 to survive the 36-hole cut and among those missing it were Phil Mickelson, Rickie Fowler, Jim Furyk, Ernie Els, Nick Watney, Ian Poulter and Vijay Singh, who earlier this week sued the PGA Tour in a complaint involving the circuit's investigation of his use of deer antler spray.
Garcia, whose most recent of eight victories in the United States came last year at the Wyndham Championship, began his birdie run with a 14-foot putt at the second. Over the next four holes he made putts of 7, 8, 19 and 26 feet.
Woods highlighted his round by making an eagle at the par-5 second, but bogeys at the seventh and 14th holes prevented him from taking the lead.
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UPI Sports Results for September 19, 2014