“I’ve been driving the ball really well, and this course there's a big premium on hitting a lot of fairways,” said Kapur, who is still searching for a maiden European Tour title.
“The driver has been behaving and I gave myself quite a few chances. Overall I just played quite solid.”
Lurking just three strokes back was Rory McIlroy after he set up the possibility of a special Sunday for himself and girlfriend Caroline Wozniacki.
The 22 year old Northern Irishman fired a second round 65 to improve from 42nd to seventh, while tennis World Number One Wozniacki is two wins away from joining him as a US Open Champion.
After all the rain delays in New York she will now play her semi-final against Serena Williams on Saturday, with the final being pushed back to Sunday.
World Number Two Lee Westwood was also in the hunt and would have matched his Ryder Cup teammate's 135 aggregate but for a late three-putt bogey in his 66.
McIlroy's priority after he finished was to make sure there were no more ants on him.
His final drive ended close to an ant-hill and although he was able to move his ball away - and had a much easier shot as a result - he said: "I still feel there are some going up my legs.
"I don't feel I drove the ball particularly well. There were a couple of loose shots and I got some lucky breaks."
Like McIlroy, Westwood had four birdies in seven holes on the back nine, but his only gain on the outward half was a two on the short fifth and his dropped shot came two holes later.
Defending champion Martin Kaymer looks certain to miss the halfway cut. Double-bogey sixes on the sixth and seventh left him six over with seven holes remaining and he probably needed to birdie all but one of them.