The former world number one showed glimpses of the form which has seen him win 14 major titles by firing two eagles and four birdies to move onto eight-under-par overall.
Woods, who hasn't won a tournament since the Australian Masters in 2009, could have been even further ahead at the halfway stage had he not carded a double bogey at the 15th.
The 35-year-old's form saw him fly past overnight leader KJ Choi, who carded a one-over 73 which included a quadruple seven at the 15th, to move back to five-under overall.
Choi is joined by Matt Kuchar in a share of second after the American carded a round of 67, including seven birdies.
Elsewhere, England's Paul Casey improved on his opening round 79 with a 68 to move to three over, while Scotland's Martin Laird is seven over after a second round 74.