Playing his fourth tournament in a row in Japan, Jeev had as many as six birdies, but his closing bogey, only the second one in the round, spoilt what was otherwise a fine round.
Jeev, a four-time winner on Japan Tour, is two behind joint leaders -- the 2009 champion Yuta Ikeda (66) and Yuki Sato -- while Taichi Teshima (67) was third.
Jeev shared the fourth place with Ryo Ishikawa (68), Shigeki Maruyama and three others.
He opened with a birdie and added a second one on the fourth hole. He turned in two-under but then bogeyed the tenth. Jeev then went into a birdie spree with four in five holes between 13th and 17th. He birdied the 13th and 14th and then again 16th and 17th. But the closing bogey left a bitter taste.
Ikeda played a flawless round with six birdies, while Sato opened with a bogey on first and then seven birdies, including four in a row from 13th to 16th. Ishikawa had five birdies and one bogey.
Jeev has played three events in Japan this year and his best result was tied 17th at the Tokai Classic.