Kapur, who looked on his way out with a card of 76 on first day putted way better than the first day on his way to 68, which made sure he was in action over the weekend.
He was tied 43rd at the end of the second, while Jeev Milkha Singh overcame a major lapse with four bogeys in a row from sixth to ninth and then had yet another bogey on 14th, he looked for an early exit at three-over.
At the top Spaniard Alvaro Quiros landed two eagles in a round of 67 to get into a three-way lead with Frenchman Victor Dubuisson and England's Eddie Pepperell at the halfway mark.
On a day dominated by the strong winds at PGA Sweden National, big-hitting Qurios eagled the par five 11th hole - his second after starting on the tenth tee - and also made a three on the first hole, added to birdies on the 15th and 18th holes, to move to six under par.
World No 2 Henrik Stenson delighted the home fans when he moved to the top of the leaderboard on seven under par with consecutive birdies on the 14th and 15th hole.
But he finished with a round of 70 and at five under par he is only one shot back going into the weekend. He is tied fourth alongside compatriot Jens Dantorp (73), Thailand's Thongchai Jaidee (70), Welshman Bradley Dredge (70) and Scottish pair Stephen Gallacher (72) and Chris Doak (69).