Jeev was two strokes behind the surprise leader Alexander Noren of Sweden, who upstaged the big guns with a stunning eight-under-par 64 at the Kuala Lumpur Golf and Country Club.
Jeev, the two-time Asian Tour Order of Merit champion, shares the third place with Darren Beck of Australia, who has won once in the region, and Stephen Gallacher of Scotland.
The Chandigarh golfer sank six birdies against one bogey to wrap up an eventful opening day, which was suspended due to lightning.
"I played well today. I started off well too. Had a lot of birdie chances, hit a lot of greens. One errant shot with the driver on seven, went for it and ended in the right and got my only bogey," he said.
"I made six birdies. I birdied 14 which is a tough hole, birdied 17 and 18 to go to three under and got three more birdies on the back, five and six.
"I thought Hole seven was a birdie hole today as it was going downwind but didn't hit it enough and it was a tough up and down from the bunker. Then I converted a 15-footer on the last.
"I'm pleased, I'm happy with how I hit the ball. I had good distance control with the irons today and I rolled the ball well. I'm pretty pleased with the round and we''ll go from here for the next three days," he added.
Jeev, who has been battling with injuries, said he was being careful with his back and would have to work with his drivers more.
"In Morocco, I had a few good rounds. I need to be more consistent with this. I need to work more with the driver.
I''ve been so protective of the back that I don't give a lash with the driver. But I have to if I'm back in the game. I'm going to start hitting more drivers now," he said.
Things were not so great for the other Indians in the fray, as Shiv Kapur (71) in tied 35th place was the only other Indian under par.
Jyoti Randhawa (73) and Gaurav Ghei (73) in tied 68th, Gaganjeet Bhullar (74) in 99th, Anirban Lahiri (75) and Digvijay Singh (75) in 121st, Sujjan Singh (78) in 141st and SSP Chowrasia (79) in 148th have a uphill task to make the cut.
The day belonged to Noren who edged past early leader, Italian teen sensation Matteo Manassero (66), while young Irish star Rory McIlroy overcame his Masters Tournament hangover with a solid 69. His score was matched by reigning British Open champion Louis Oosthuizen of South Africa.
World number one and PGA Championship winner Martin Kaymer of Germany, playing alongside McIlroy, fired a 70 while newly crowned Masters winner Charl Schwartzel of South Africa struggled with fatigue and jetlag to card a one-over 73.