The 29-year-old Woodland, who earlier this month won the Reno-Tahoe Open for his first PGA Tour title, was four under par for the round and 13-under for the tournament, the opening event in the FedExCup playoffs.
Little known Kevin Chappell also used a blistering hot spell to leap up the leaderboard, making seven birdies in an eight-hole stretch to reach 10 under par with two holes to play in his round.
Moving Day lived up to its name in Saturday's third round after Matt Kuchar claimed a two-shot lead in completing a second round 65 in an early morning return along with 39 other players after play was suspended on Friday due to failing light.
Bogeys at the third and seventh holes dropped Kuchar to nine under par, four shots off the pace.
Webb Simpson, the 2012 U.S. Open champion who had been tied for second with Woodland at the halfway mark, bogeyed the sixth and eighth to fall into a tie for fourth on eight-under with fellow American Rickie Fowler.
Fowler had used an eagle at the par-five sixth to move into a temporary share of the lead at 10-under but double-bogeyed the ninth after an errant tee shot.
World number one Tiger Woods also moved in the wrong direction. The FedExCup points leader began the round at six under par and birdied the first to reach seven-under, but three bogeys in a five-hole stretch left him five-under through 12.
Tied for sixth at seven under par, six behind Woodland, were a group of seven including U.S. Open winner Justin Rose (through 12 holes) and fellow Englishman David Lynn (12), former Masters champion Charl Schwartzel of South Africa (11), Australian Aaron Baddeley (15) and Spain's Sergio Garcia (11).
They were joined by Americans Jim Furyk (13) and 20-year-old Jordan Spieth (15).
Players teed off in threesomes off both nines for the third round at the scenic course waterside course with views of the Statue of Liberty and the Manhattan skyline.