Woodland fired a wedge shot within 18 inches at the final hole to cap off a four-under-par 68 at Albany Golf Club on the island of New Providence.
At 13-under 203, he goes into Saturday’s final round ahead of Swede Henrik Stenson, whose lead evaporated with a bogey at the last.
Woods birdied the last for a 67, joining Justin Thomas and defending champion Jon Rahm on two back.
Halfway leader Patrick Reed received a two-stroke penalty for improving his lie in a sandy waste area at the 11th hole.
He brushed the sand twice on practice swings and was deemed to have improved his lie.
U.S. Open champion Gary Woodland birdied the final two holes for a one-shot lead after the third round at the Hero World Challenge in the Bahamas on Friday as tournament host Tiger Woods lurked two shots behind.