Kapur, with a total of eight-under 134, is now three behind leader Joel Sjoholm of Sweden, whose rounds of 67 and 66 gave him a total of 11-under at the top.
But the two other Indians in the field, Jeev Milkha Singh (72-72) and SSP Chowrasia (75-69) missed the cut as they finished tied 71st for two rounds.
"If I keep the putting the way I am and I keep hitting the fairways and greens I am fine. I feel I have good speed of the greens this week. I changed drivers from yesterday. I hit a few more fairways," said Kapur.
"Pars are good scores and any birdies are a bonus. The 20-foot par almost dropped on the last. It is not often that you stand on a 20-foot putt and expect it to fall, but today I did. It almost dropped. Still, it is a marathon not a sprint. Now the real business end of the tournament begins. I need to keep the same spirit and same attitude to keep going.
"I wanted to keep the mistakes off the card. The ninth and 18th are tough holes. Starting out, I knew it was going to be tough, but golf is a bit greedy, you just keep wanting more," he added.
The 27-year-old Chilean-born Sjoholm, adopted by a Swedish couple when three months old, eagled both the 577-yard 16th and 546-yard third hole for a superb six-under round in the windy conditions here.
He was two clear of overnight joint-leader Fabrizio Zanotti, former Ryder Cup star Paul McGinley and English pair Danny Willett and Chris Wood.
Local favourite Martin Kaymer, the highest-ranked player in the field, missed the cut, but 54-year-old compatriot Bernhard Langer shot 67 and at five under is not out of the hunt yet.
