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He carded a three-under-par last-round 69 to finish three strokes clear of South African Eric van Rooyen in an event that stretched to five days because of bad weather.
The final round was suspended Sunday due to torrential rain, lightning and hail and resumed Monday at 0730 local time (0530 GMT).
Sharma birdied three holes on the outward trek, then parred all the inward-nine holes with immaculate approach shots and putting highlights of his game.
After three bogeys during his opening-round 69 last Thursday, Sharma played 55 holes without dropping a shot and his second-round 61 was the lowest score of the tournament.
Visa delays and tiredness after a long Asian Tour campaign left the 21-year-old Indian contemplating missing the tri-sanctioned European Tour, Asian Tour and South African Sunshine Tour event.
His late decision to visit South Africa for the first time paid rich dividends as he pocketed a 2.6 million rand ($190,000/160,000 euro) first prize.
Victory also guaranteed Sharma, along with Van Rooyen and joint third Shaun Norris of South Africa, places at the 2018 British Open in Carnoustie next July.
“I am thrilled that I came to the Joburg Open,” said Sharma after adding to five victories on the Indian circuit.
“It has been a very long Asian Tour season for me so I was considering whether I wanted to visit South Africa. I am really happy that I did.”
The previous best European Tour finish for the golfer ranked 462 in the world was sharing ninth place at the Maybank Championship in Kuala Lumpur last February.
“Winning the Joburg Open on my first trip to South Africa is a wonderful feeling,” Sharma said after receiving the trophy from Johannesburg mayor and golfer Herman Mashaba.
“I met my caddie for the first time last Monday and we worked so well together. Heeding his advice was a key factor in my success.
“Saving par on a number of holes thanks to up and downs played a significant role in keeping me at the top of the leaderboard.
“It has been absolutely fantastic and the people were very welcoming. I do not think I will ever forget this week.
“This is my first win on the Asian Tour and the European Tour so it means a lot to me,” said Sharma.
“On the first day there were 240 players. I was just trying to play two good rounds to make the cut, which was really low.
“I was playing well and had a great start on the second day which got things going for me. As soon as I reached 13 under after two days, I thought I had a chance to win.
“The only thing I was telling myself was to stay aggressive. I never wanted to be defensive.
“Even when I was in front I never thought of defending my lead. I actually set a target of 25 under.”
Van Rooyen quickly became the only final-round threat to Sharma and five outward-nine birdies narrowed the gap to four shots by the turn.
But he could add only one further birdie, leaving steady Sharma to succeed one week after compatriot Arjun Atwal finished runner-up in the Mauritius Open.
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