Jeev has a two-day total of one-under 140. After parring the first couple of holes, Jeev struck a birdie on the third and gained two more shots on the fifth and seventh to make the turn three-under.
The back-nine started disappointingly as he stumbled to a bogey on the 11th hole but he made amends with a birdie on the 12th hole.
But his card was marred by bogeys on the 16th and 17th as he settled one-under for the day.
At the top, Columbian Camilo Villegas (66) and American Anthony Kim (64) shared the lead with totals of eight-under 132.
Fijian Vijay Singh (66) followed them a stroke adrift at the lone third spot.