Jeev continued to the best of the lot at two-under for 54 holes, while SSP Chowrasia was a picture of consistency with three identical rounds of even-par 72 each.
Gaganjeet Bhullar (74, 73, 69) was also at even-par, while Anirban Lahiri shot rounds of 78, 70 and 76.
Michael Hoey, a four-time winner on European Tour, was six-under through 14 holes in the third round, but he was four shots clear of the second placed defending champion Alexandre Kaleka (67) and Mathew Nixon, four-under through 15 holes.
Jeev, who was three-over for front nine, went to three-under on back nine to card 72.
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Chowrasia and Bhullar were tied 39th and Lahiri was lying tied 64th. Shiv Kapur, who made the cut at the British Open last week, was the sole Indian to miss out after rounds of 76 and 76.
Swede Rikard Karlberg, whose two big international wins have both been on Asian Tour and in India, carded a fine four-under par 68 in tricky, swirling winds to give himself a two-shot lead after the second round.
The 26-year-old moved to nine-under at the halfway stage of the tournament, two strokes clear of England's Matthew Baldwin, France's Alexandre Kaleka, China's Liang Wen-chong and Northern Ireland's Michael Hoey.