Starting in the morning session, Kapur had one birdie, one bogey and seven pars in a display of steady golf.
Kapur teed off from the tenth and had three pars before finding his first birdie. On the par-4 13th playing to 391 yards, Kapur drove with a 3-Iron and followed that up with a superb second shot with 9-Iron to landed within six feet.
He duly holed it for his first birdie. Following up that birdie with four more pars, he came to the ninth, where he missed the green in regulation.
The early leader was Matt Kuchar at three-under through 13, while Korean-American Kevin Na was second at two-under through 14 holes. Jordan Spieth, tied second at Masters, was one-under through 11 as were Henrik Stenson (through 13), Phil Mickelson and Graeme McDowell, through 12 each.
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Yesterday, Pinehurst No 2 was fortunate to avoid the storms that swirled around the area, so the greens, which were well-watered stayed healthy giving the morning starters a good advantage.
The green speeds are averaging 12 and a half feet on the stimpmeter and they received more water on Thursday morning before play.
Thongchai Jaidee, the top Asian in the field was two-over through 11 holes. In the second round, Kapur will tee of at 2:20 pm in the afternoon.
The 32-year-old Kapur, had on the eve of the tournament said,"It's always been a boyhood dream of mine to play in the US Open especially since I went to college in America and came agonizingly close to qualifying back in 2004 when I was still in college. So now that I'm there I'm going to soak in the whole experience and live the dream."