Kapur, who was overnight tied 27th, finished a stroke below the cut-line after a roller-coaster three-over 75 left his total at 144.
Kolkata-pro Chowrasia was three strokes adrift of Kapur after carding a 76, while Randhawa (74) was further down the leader-board with a total of 154.
One-over at the turn after managing one birdie against a couple of bogeys, Kapur's back-nine turned out to be a topsy-turvy affair.
The Delhi golfer found a birdie on the 10th but stumbled to back-to-back double-bogeys on the 11th and 12th holes. Kapur pulled off consecutive birdies on the next two holes but again floundered with a double bogey on the 15th.
After parring the 16th, Kapur needed to sign off with successive birdies to make the cut but he could manage only one. Chowrasia, meanwhile, fetched just two birdies against four bogeys and a double bogey in his card.
Randhawa, on the other hand, found five birdies but was undone by three bogeys and a couple of double-bogeys sandwiched in between. At the top, England's Luke Donald took the sole lead with a total of 12-under 132 after returning a 67 in the second round.
Welshman Rhys Davies (68) was a stroke adrift of Donald at the second spot.