On Friday, Kapur shot 7-under-par 65 and Park a 6-under 66. Their 36-hole total is 10-under 134.
Neither has ever held a 36-hole lead in a European Tour event, which is especially important to Kapur, a New Delhi native.
Kapur's round Friday included five birdies and an eagle at the par-five sixth hole.
"I got off to a good start with an eagle on front nine and a couple birdies and I seemed to be putting pretty well," Kapur said. "I rolled the ball well and made all the putts I needed."
In all, 25 players are within five shots of the lead.
Swim Week Miami Beach 2014 [PHOTOS]