Playing at the Omega Dubai Desert Classic after a gap of two years, Kapur was tied 69th, while Jeev and Bhullar were in danger of missing the cut at 111th and 125th after the opening round here.
Even as the Indian trio struggled at the Emirates Golf Club, Rory McIlroy 'made hay while the sun shone' and produced a masterly display and led a string of low scoring performances with a nine-under 63.
Quesne ended at 66 and in a tie with four others, including defending champion Stephen Gallacher.
Tiger Woods playing in the same group as McIlroy and Gallacher, carded a bogey free four-under 68.
More From This Section
Kapur had a fine start with a par on first and birdie on second, but he gave that shot back on sixth. Thereafter he had numerous birdie chances, but he could not capitalise on them.
He later said: "The conditions were scoring friendly but I just didn't make enough putts. It was not quite the start I was after but my game feels good and with a good round tomorrow I can be in the mix for the weekend."
Jeev had a difficult time too as he made five birdies but dropped as many as eight bogeys.
"That was unbelievable number of bogeys," he said.
Bhullar, making his debut in Dubai, was disappointed with his putting. "I was playing well and hit the ball decent. But I just could not get the putts to fall. It was the same story right through. I just managed two birdies late in the day on 14th and 17th, but I am hoping to make up tomorrow.