Chawrasia finished in a tie for fifth at 18-under 270, while Norris won the title at 24-under 264 with rounds of 66, 66, 61 and 71.
Norris won despite a major stumble as he gave his rivals a chance with four bogeys in a span of six holes on the front nine.
The 33-year-old South African, staggered to three bogeys from seventh to ninth and allowed the seven-shot lead to come down to three. But Norris was strong enough to pick up the pieces yet again with three birdies on the return journey and then calmly parred the last three holes for his second career win.
American Casey O'Toole (67) who brought himself into the mix with a third round 63, tied for fifth with Chawrasia.
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Rahil Gangjee (72), who was playing the third successive day while being unwell was unable to produce the magic of last two rounds, when he shot 66-66.
Gangjee, after birdies on fourth and fifth, faded away with three bogeys and just one birdie and ended in a tie for 15th.
Himmat Rai (69) rose a bit, while Arjun Atwal (73) and Rashid Khan (73) slipped down and all ended in a tie for 26th at 10-under 278 and Shiv Kapur (71) was tied 35th at nine-under 279.
Chawrasia was gracious as he said, "Congrats to Shaun (Norris). He held on to the lead despite that string of bogeys in the middle. Yano and Park have him a good fight but this was Shaun's week after that great third round.
"I know I could have been better this week, but tied fifth is alright. Still it was nice to end the week with a birdie. On 18th I went into a bunker into the face and then got out from there into left rough. My third shot went just over. I had a 30-foot putt from edge of the green and it went in perfectly for a closing birdie," he added.
It was the second career win for Norris, who as opposed to just one birdie in first 54 holes, made four in a span of six holes, including three in a row from seventh to ninth. It also opened the doors to Japan for Norris, as the event was co-sanctioned with Japan Golf Tour.
Norris said, "The conditions were not easy from the start. When I stepped out of the hotel this morning, it was gusty and it was blowing. I knew scoring was not going to be easy. I tried to give myself chances early but I hit several bad shots in the wrong places. The wind really got me in the front-nine and confused me."
Norris, who was one the last players to discard the now-banned broom, continues to use a long putter but manages to do it without anchoring it. The Pretoria-based golfer who came through the Qualifying School last year, won his maiden Asian Tour title at the Yeangder TPC barely four months ago in October, 2015.