He shot a three-under 68 after being in sole lead at six-under at the turn. It was the first time ever that an Indian held the sole lead at any stage in a Major.
At three-under 68, he was two shots behind Zach Johnson, the 2007 Masters champion, and just one behind a Rafael Cabrera-Bello and veteran Mark O'Meara, who shot 67 each.
Kapur making only his second appearance at a Major -- his first was at the Open in 2006 -- had a sensational start with three birdies on the trot.
After a par on the fourth hole, he birdied the next three and wowed the crowd as he held sole lead at six-under after seven holes.
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A double bogey on 10th followed by a bogey on 14th dropped him to three-under and tied fourth at the end of the day.
There was even talk in the media centre looking for the lowest ever round at a Major -- it was 63 by Rory McIlroy at 2010 Open -- but then with three dropped shots on back nine, Kapur began to look more human.
Ranked 210th in the world, Kapur would hardly have been the choice to pick for a first round leader but undeterred and not awed by the occasion and followed by his family and friends, he played calmly and kept his cool even when he double-bogeyed the 10th and bogeyed the 14th.