Garcia, the 2008 champion, vaulted to the top of the leaderboard on Friday with a seven-under 65 that included five consecutive birdies and gave him an 11-under total of 133.
One stroke back was Woods, who fired his second successive 67 in his quest for a second Players Championship title and fourth win of the 2013 season.
"I don't have to measure myself against anybody," said Garcia. "I know what I want to try to do and any given day, I can shoot a round like this and any other day he can shoot a good round and beat me."
The two players first locked horns at the 1999 PGA Championship, when a then 19-year-old Garcia challenged 23-year-old Woods down the stretch at Medinah in what seemed to promise the first great golf rivalry of the 21st Century.
Garcia, who had won over fans at the Chicago suburb with his bubbly personality, burst back into contention that week from five strokes down with seven to play on a three-shot turnaround on the 13th, where Garcia birdied and Woods took a double-bogey.
The Spanish teenager gave Woods a challenging glare when their eyes met after Garcia's long birdie putt at the par-three.
"I was kind of telling him - if you want to win, you have to play well," Garcia said afterward.
Then on 16, Garcia thrilled the fans with an eyes-closed swipe at his ball lodged between roots of an oak on the right side of the fairway and an exuberant sprint up the fairway to see it stop, incredibly, on the green.
Woods stepped up and made a treacherous, eight-foot downhill putt at the 17th to preserve his one-shot lead and parred the last to hold on for the victory, his second major title following his record-setting, runaway win at the 1997 Masters.
Since then, wins on the biggest stages of golf have mainly gone to Woods, who has collected 14 majors as the greatest player of his generation, while Garcia is still looking for his first after some heart-breaking losses.
Garcia, who has garnered eight career U.S. tour wins and 15 international victories, has mellowed over time but does not want for confidence.
"Like we always say, it's not a sprint, it's a marathon," Garcia said about his chances to add his name to the list of multiple winners of this championship, which is often referred to as the fifth major.
"So just got to enjoy the good ones as much as possible."
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