Stenson, who led after the first round was completed earlier Friday with an 8-under-64, turned in a 68 in the second round. Victor Dubuisson had a second-round 65 and Ian Poulter and Justin Walters each shot second consecutive 66s, leaving a four-way tie for first at 12-under 132.
Woods, who completed his first round at 2-under, fired an eye-grabbing 9-under 63 in pulling within one stroke of the leaders. Woods' first round included bogeys at Nos. 9 and 18 but the second featured birdies at those holes along with seven others.
He ran off three consecutive birdies over Nos. 2-4 and closed with three birdies in the final four holes.
Stenson, playing alongside Woods and Justin Rose, opened his second round with nine pars. He was 4-under on the second nine, with an 18th-hole birdie that pulled him into the first-place tie.
Dubuisson's second round was fired by consecutive birdies over Nos. 10-13 and included a bogey at 17.
Poulter had four birdies in the final six holes of his bogey-free second round while Walters' card was dotted with nine birdies and three bogeys.