Randhawa, overnight tied fourth with an opening round of 67, sank in three birdies and an equal number of bogeys in the second round to total five-under 139.
Kapur, on the other hand, is unlikely to make the cut, to be decided after the third round, with a total of three-over 147 so far.
Randhawa was off to a steady start as he parred three holes before picking up his first birdie on the fourth. But a bogey on the seventh hole left him even-par at the turn.
The seasoned pro's back-nine comprised bogeys on the 10th and 18th with birdies sandwiched in between on the 12th and 14th holes.
At the top, Rory McIlroy fired a seven-under 65 to earn a share of the lead with fellow Northern Irishman Michael Hoey (66) and Scot Richie Ramsay (66). The trio is 11-under overall.