The Inverness-born Knox, who is contesting the lucrative FedEx Cup Play-Off Series for a first time, shot two-under-par 69 to move to a clubhouse share of sixth place on six-under par in the $8m event on the Ridgewood Country Club course.
It left Knox trailing just two shots behind the defending champion Adam Scott (65) and the American Cameron Tringale (68) who shared the lead at eight-under par.
However, Knox was left reeling early in his round when he doubled the third hole from a greenside bunker before brilliantly redeeming himself, holing his 7-iron second shot from the fairway for an eagle 'two' at the par-four fifth.
He bogeyed the ninth but Knox cut a swathe through the field with three closing birdies including landing another 7-iron to two feet at the last.
"I am delighted but then my score doesn't reflect how well I played out there today as it was up there with the best I've hit it all year," said Knox. "I just gave myself chance after chance and [that was] with my putter ice-cold at the start, so to end with three birdies was very pleasing. This has been a breakout year for me so it would be nice to cap it off with a win."