Jeev, who shot one-over 72, carded four-under 67 to get to three-under 139 and make the weekend rounds. His round included an eagle and a birdie in the last four holes.
Meanwhile, Shiv Kapur missed the cut as he carded a 76 and 70 in his two rounds.
At the top, Alexander Levy stormed into the lead on day two with a stunning 10-under 61, but the Frenchman was one of only two groups to complete the second round after thunderstorms and heavy rain severely disrupted play, forcing the tournament to be reduced to 54 holes.
The majority of players will now have to complete and, for half the field, start their second rounds this morning, and Levy faces a strange situation where he will now not play until the third and final round on Sunday.