Kuchar came into the day with a two-stroke advantage, but registered a 1-under 70, ending the day tied with Woodland at 12-under-par 201.
Both golfers had to complete their second rounds earlier in the day due to weather delays caused by rain Thursday.
Kevin Chappell shot a course-record 9-under 62 to jump into sole possession of third place.
Tigers Woods, battling a stiff back, managed a 2-under 69 to join David Lynn (69) in a fourth-place tie at 8- under 205.
2014: The Year in Music [PHOTOS]