Kapur shot a course record seven-under-par 65, while McArthur moved back into second place after signing for a one-under-par 71 to move to nine under for the tournament, with a round featuring three birdies and two bogeys.
"I actually played really well," said the 33-year-old. "I didn't putt as well as previous days and had three three putts from the fringe, so that was disappointing. I seemed to get really tired out there but I played good golf for the most part. Shiv just played great. I just need to get off to a quick start, do the same as I did on the first day, when I got a few 30 footers and hit a few right at the pin. You want to be within a couple going into the back nine to get among it."
Kapur's outward nine featured birdies at the first, third, fourth, sixth and ninth holes, before another at the 10th brought him a four-shot lead. The 30-year-old's return leg included an up-and-down for a birdie at the 14th, before four successive pars, to move him to 13-under for the tournament.
"I can't complain with a course record," said Kapur. "I needed to take the tournament by the scruff of the neck and I think I managed to."
England's Philip Archer is a shot behind McArthur on eight under par.