Jeev, who was tied 40th overnight, rose up the leader-board with a two-day total of three-under 141.
One-under at the turn after slotting two birdies against one birdie in the front nine, Jeev played out a flawless back-nine studded with back-to-back birdies on the 10th and 11th holes.
In contrast, Kapur bowed out after a disastrous back-nine.
After dropping a bogey on the seventh, Kapur struck a magnificent double eagle on the par-five ninth to make the turn one-under.
But he ended up dropping six bogeys in a miserable backward journey to bow out of contention.
At the top, the American duo of Robert Garrigus (65) and Matt Bettencourt (68) shared the lead with totals of 10-under 134. Their compatriot John Mallinger (67) occupied the second spot with a total of 136.