Bhullar added a 69 to his first round 68 to move to five-under, while Kapur played a wobbly 71 to be four-under after 36 holes.
The halfway cut came at three-over and a total of 81 golfers, including 21 Indian professionals and five amateurs made the weekend rounds. Local lad S Chikkrangappa (72-68) is among five amateurs who made the cut.
Richie Ramsay of Scotland birdied four of his last five holes to fire a 66 and race to a three-shot lead ahead of three players including Thai duo Panuphol Pittayarat and Chapchai Nirat, and Jaakko Makitalo of Finland.
The bunch in second place all returned matching 68s.
In-form Bhullar, who won his fourth Asian Tour title in Macau last week, led the local charge with a round of 69 for tied sixth position and is five shots off the pace.
Bhullar has kept his bid for the title alive as he peppered the greens with acute iron play.
More From This Section
"I felt good and was enjoying myself because I found a lot of fairways and hit a lot of greens in regulation. I'm still looking forward to hitting some low numbers in the next two days," said Bhullar, currently in fifth position on the Order of Merit.
"I had a great start with three birdies on the trot in my first four holes, but then on the second nine, the front side of the course, I had a bit of a wobble that cost me three shots. That left me a lot of work to do over next two days," he added. (MORE)