Jeev, a former champion here, was one-under through 12 holes before dropping bogeys on the 13th and 17th to finish at 73. He slipped to tied 30th on the leaderboard at two-under 214.
Bhullar, who had survived the cut with a fine fightback, gave away two shots on the 16th and 18th to finish the day at 72 and one-under 215 in tied 40th place for the week.
He was two-under through 13 holes before slipping down on a blustery day.
A hat-trick of birdies from the sixth saw the Australian catch overnight leader Mikko Ilonen, and the Finn bogeyed the last after driving into the water at the Binhai Lake Golf Club to hand Rumford the lead.
Defending champion Branden Grace -- ironically the last player to win two weeks running on the European Tour in his native South Africa last January -- is nine back after a third round 72.
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