(CNN) -- Tiger Woods will go into the final round of The Barclays four shots off the lead after completing his second successive round of two-under-par 69.
It marked a slight improvement after the world No. 1 ended his rain-delayed second round five shots behind the same pacemaker, Matt Kuchar, earlier Saturday.
However, Kuchar -- who can move to the top of the FedEx Cup standings above current leader Woods if he wins the $1.44 million first prize -- was caught at the top by fellow American Gary Woodland after 54 holes.
Kuchar carded a third-round 70, while Woodland went around two shots better to join him on 12 under.
They were one shot ahead of Kevin Chappell, who broke the course record at Liberty National in New Jersey with a flawless nine-birdie 62. It was the second time he has posted that score this season, and lifted the 27-year-old up from 43rd place at the halfway stage.
Kuchar, 35, triumphed at The Barclays in 2010 when it was played at Ridgewood Country Club, and is seeking his third victory this year.
Woods -- who has won a leading five times on the PGA Tour in 2013 -- moved up from a tie for eighth as he birdied two of his last three holes.
He also started with a birdie, but three bogeys in five holes in the windy conditions set him back again.
However, the 14-time major winner got a shot back at the eighth hole and picked up another at 13 before a strong finish left him in a tie for fourth with Englishman David Lynn, who also shot 69.
U.S. Open champion Justin Rose was in a group tied for sixth on seven under, along with Bubba Watson, Jim Furyk and Rickie Fowler.
Masters winner Adam Scott dropped back to a tie for 13th after suffering a double-bogey in his 72.
The Australian was level with former world No. 1 Rory McIlroy, who had three birdies and three bogeys in his 71, 2012 U.S. Open champion Webb Simpson (74) and Sergio Garcia (71).
British Open champion Phil Mickelson moved up nine places to a tie for 34th after a 70, but was not happy with his game.
"I hit a lot of good shots and made a lot of good swings," the veteran left-hander said. "I was sloppy, though, and I didn't score well, and Sunday is going to be an important day for me, because I just want to put it together."
Last year's FedEx Cup champion Brandt Snedeker, in his third tournament since several months off battling bone disease, missed the halfway cut by one shot after a 71.
Graeme McDowell, Ian Poulter and Ernie Els were among the other high-profile names to also drop out in the $8 million event.