Despite that Bhullar slipped from overnight tied eighth to tied 16th.
Also making the halfway cut were Shiv Kapur (68-71) at five-under in tied 28th place and Jeev Milkha Singh (71-71) at two-under in tied 57th place.
However, Spaniard Rafa Cabrera-Bello raced into the halfway lead after a fine second round of seven under par 65.
Rafa moved to a 13-under total and establish a two-stroke advantage over South Africa's George Coetzee (69) at 11-under.
Bhullar bogeyed second and fifth but did have a birdie on third to turn in one-over. He eagled the 10th and then added a birdie on 17th to come to two-under 70.
Kapur also struggled with a bogey on par-five ninth and then with three more pars, he was one-over after 12. He birdied 13th, 16th and 17th but gave away a shot on the last at 18th for a round of 71 to go with his 68 on first day.
Jeev had three birdies and two bogeys in his 71 and he was now two-under for two days.
Cabrera-Bello, a native of the Canary Islands, felt very much at home on The European Tour's desert swing and hoped to add the Commercial Bank Qatar Masters crown to the Dubai Desert Classic title he won in 2012.
"I'm really happy, really pleased, and everything's going good so I'm enjoying myself," said Cabrera-Bello.
"Playing in the desert at this time of year definitely feels like home. I like playing in short sleeves a lot, I like a little bit of breeze, I like seeing palm trees and I like seeing sun around the courses. It does remind me a lot of the Canaries, and it's kind of like I haven't left home, so that's why I enjoy it so much," he said.


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