The world number one began the day on five-under par - three shots behind overnight leader Watney - and struggled to come to terms with the greens on the front nine at the HSBC Champions tournament.
However he came back with four birdies to move to -10 and a share of the lead with his compatriot in the Far East.
Phil Mickelson, Ryan Moore and Spain's Alvaro Quiros sit a further shot back, while English duo Paul Casey and Ross Fisher are six shots back on six-under par.
But Woods will be the man to catch, once again, at the weekend, and he admitted that the pin positions, especially on the front nine, caught him out before he rallied to share the lead.
"It was certainly a little bit frustrating," he said. "I knew that if I could just basically play the back nine at three-under par, I figured that would be a good number. And I did a couple better than that.
"I was surprised at how difficult the pins were. Consequently, the guys didn't go as low, but still there were plenty of opportunities out there."