Woods, seeking his first PGA Tour title since the 2009 BMW Championship, was standing at 11-under 205 following 54 holes.
That was one stroke better than 2010 U.S. Open champion Graeme McDowell, who also carded a 71 Saturday.
McDowell bested Woods in a playoff at the 2010 Chevron World Challenge.
Ernie Els, seeking to crack the Top 50 in the world rankings with third-place-or-better finish at Bay Hill, registered a 5-under 67 to move into a share of third at 8-under-par 208 with Ian Poulter (68).
Tied for fifth at minus-7 were Charles Howell III (68) and Johnson Wagner (69).
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