Sharma, who won the Joburg Open last month for his maiden victory outside India as a professional, had four birdies against two bogeys in the second round.
In the first round, Sharma shot one-under 71. At three- under 141, Sharma is now Tied-44th.
Sharma, teeing off from the first, ran into early trouble with bogeys on second and third, but a birdie on fifth settled him. On the back nine, he found his composure and birdied 10th and 11th and added another on 18th, just like the first day.
Rory McIlroy was part of a four-way tie on nine under in his first event since October, with world number one Dustin Johnson a shot further back.
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Ryder Cup star Pieters, who finished second in this event in 2016 and fourth a year earlier, made three birdies in an outward 33 after starting on the back nine.
Pieters birdied the first, then holed from 20 feet at the second, with two putts from just off the green at the par-five eighth providing another gain. The 25 year old found sand with both his tee shot and approach at the ninth, but chipped in from the bunker for an unlikely closing birdie.
Three of Pieters' EurAsia Cup team-mates from last week's European victory over Asia were tied for third, with France's Alex Levy, England's Ross Fisher and defending champion Tommy Fleetwood all on ten under par.