Kapur and Park are tied at 10-under 134 atop a crowded leaderboard.
Jyoti Randhawa (65) and Taichiro Kiyota (67) are one shot back at 9-under 135, with world No. 5 Adam Scott (68), Philip Archer (64), Jose Manuel Lara (67) and Graeme Storm (66) at 8-under 136.
There are 25 players overall within five shots of the lead, including Vijay Singh and overnight co-leader Daniel Vancsik.
Neither Kapur nor Park had ever held a 36-hole lead in a European Tour event before Friday. It was especially important to Kapur, who lives in New Delhi.
His spotless round included five birdies and an eagle at the par-5 sixth, where he knocked a 3-iron to 10 feet. Kapur played the front nine in just 31 shots.
'I got off to a good start and made an eagle on front nine and a couple birdies, but I just seemed to be putting pretty well,' said Kapur. 'I don't know how many putts I made today, but I felt like I putted well. I rolled the ball well and I made all the putts I needed to.'
Kapur, Randhawa and three other Indians are among the top 25 players on the leaderboard in just the second European Tour event ever held in their home country. The first was the Indian Masters three weeks ago, won by countryman S.S.P. Chowrasia.
'You are playing in your own country and people expect you to play well, you expect to play well and before you know it, you play and start scoring,' said Randhawa, who had seven birdies in a flawless round. 'I just wanted to go out and have fun and do the best I could with my game.'
Park, a Korean-born Australian, posted eight birdies and two bogeys in the second round. He collected five birdies in a six-hole stretch from the sixth, then ended with back-to-back birdies at 17 and 18.
He admitted making a swing adjustment this week after watching a notorious range hound practice at DLF Golf and Country Club.
'I was watching Vijay (Singh) on his backswing and he keeps his head really still,' said Park, 'I tried to do similar things as I move my head a lot. I just tried to stay steady and it is working.'
Shamim Khan, an Indian who shared the first-round lead with Vancsik, missed the cut by a shot on Friday after shooting a 76 to post 1-under 143.
Also missing the cut were Chowrasia, Ian Poulter, Paul McGinley and Colin Montgomerie.