Former world number one Woods, who had spinal-fusion surgery last April and only returned to the PGA Tour this year, made his only bogey of the day on his final hole for a three-under-par 68 at Innisbrook Resort's Copperhead course.
That left the 14-times major champion at four-under 138, level with fellow American Brandt Snedeker (68) and Englishman Paul Casey (68), who birdied his final hole.
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Sean O'Hair carded a 68 to lie a further stroke adrift at three-under while overnight leader Corey Conners, a rookie from Canada who set the pace with a 67 during a windy opening round, was scheduled to tee off at 1:30 p.m. ET (1830 GMT).
For Woods, who is playing in what is likely his penultimate event ahead of the April 5-8 U.S. Masters, the round marked yet another encouraging outing for a player who has seen abrupt injuries make prior comeback attempts short-lived.
Woods, who started on the back nine, birdied his third and fourth holes before adding another pair on the back nine. He did well to keep his bogey-free streak alive at the par-four seventh after sending his chip about 12 feet past the hole.
But at his final hole, the par-four ninth, Woods' par putt from about five feet lipped out, denying him a chance to hold the outright clubhouse lead.
Woods, 42, returned to the PGA Tour in January and in his first event earned a share of 23rd at Torrey Pines. He missed the cut at Riviera but enjoyed his most promising result since 2015 when he finished 12th at the Honda Classic two weeks ago.
Woods' two playing competitors in a marquee group, three-times major champion Jordan Spieth (71) and Swedish world number 14 Henrik Stenson (74), were well outside the projected cutline of two over.
Masters champion Sergio Garcia, who was level with Woods after the opening round, was among the late starters on Friday.
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