Bhullar, who slipped to tenth after being tied second at the start of the final round in Abu Dhabi, teed off from the tenth and fired three birdies in a row, before adding two more on the stretch to turn in five-under.
Thereafter he had just one more birdie and a lone bogey second and was three behind leader George Coetzee (64).
Shiv Kapur, who returned to the European Tour this year, tied 37th last week, and was four-under through 16 holes. He had four birdies in his first seven holes and played pars on the rest. Jeev Milkha Singh carded one-under 71.
Coetzee had an eagle on 10th besides seven other birdies and a bogey, while Van Der Walt had an eagle on first, his tenth hole, and five other birdies and no bogeys.
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Webster's card was highlighted by a stunning albatross on par-five 10th, which was his first hole. He holed a five-iron from 245 yards and later said: "There were two people behind the green and one of them started jumping up and pointing down so I didn't know if it had gone over the back into the rocks or 'in'. I've never been three under after one before."
Bhullar, who has five titles on Asian tour against his name, was happy with his round. "I got off to a good start and was three-under after three. It felt nice flying in a short distance and conditions were good. I have been hitting well for last few months and even though it (today's round) could have been better, I happy still happy with the 67.