Garcia, Woods and Westwood led a scoring parade as eagles and birdies flew all around TPC Sawgrass on a steamy day in what is widely regarded as golf's unofficial fifth major.
Garcia, the 2008 champion, fired a sizzling seven-under 65 to post an 11-under total of 133 that left him one shot ahead of Woods (67), who sank an 18-foot birdie putt at his final hole, the par-five ninth.
Another shot back was Westwood and 26-year-old American Kevin Chappell, who shot matching 66s.
Roberto Castro had set the pace in the opening round with a course-record-tying nine-under 63 for a three-shot lead, but the little-known American's advantage vanished before he teed off in the second round's afternoon wave.
World number one Woods, rounding into top form this year with a tour-leading three victories, began the day four shots back but gained a share of the lead at nine-under when he sank a 20-foot eagle putt on the par-five second, his 11th hole.
He surged into the lead with a birdie two holes later and was joined at 10-under by Garcia when the Spaniard capped a streak of five consecutive birdies by rolling in a 26-footer at the par-three sixth, his 15th hole of the day.
Garcia climbed to 11 under par at the par-three eighth when he drained a 40-footer for birdie.
Woods lost a stroke when he bogeyed the par-four seventh after driving into the right rough but the 14-times major winner made the shot back with his closing birdie.
Westwood, also starting on the back nine, jump-started his round with an eagle at the par-five 11th and birdies at the next two holes.
Flying the banner for the lesser-known players, Chappell's round also included an eagle at the 11th.
Australian Marc Leishman got into the act with an unusual eagle, holing out from 172 yards at the par-four 18th that left him with a six-under 66 and a two-day 138 total.
Four-time major champion Phil Mickelson was in danger of missing the cut, projected at one-under, after his one-over 73 left him with a one-over total of 145.