The 21-year-old Sharma, who won the Jo'burg Open last month for his maiden triumph on the European Tour, had a rough start with two bogeys in his first six holes.
He managed to find a birdie on seventh to finish his front nine in one-over. But his fortunes turned on the back nine, when a superb third shot landed him an eagle, which gave him the momentum he needed.
SSP Chawrasia fired a two-under 70, which included three birdies just after the turn on 10th, 13th and 14th.
Earlier, he birdied the second, but he had bogeys on sixth and 16th. He was on the edge at tied-69th and needed a solid second round to secure his weekend place.
Sharma said:"I didn't have a great start and dropped two early bogeys on second and sixth and I was struggling a bit. Then came the eagle on the tenth where I had a perfect shot which landed near the cup and rolled in for an eagle.
Jamie Donaldson was in the lead with a superb 10-under 62 that may well have been better but for the bogey on the 18th. He has eight birdies, four on the back nine, which was his first nine, and there was an eagle, too.
On his second nine, he had five birdies and a bogey in the closing hole.
Earlier, David Horsey fired a 63 to set the clubhouse target before it was overtaken by Donaldson. Also shooting a 63 was Anthony Wall, while Tyrell Hatton shot 64.
McIlroy, a two-time winner here, has not finished outside of the top-10 in Dubai since claiming his first European Tour victory in 2009.
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