Dwivedi (67-73-73) and Aman (70-72-73) had made the cut out of the six Indians who started the competition.
"It was indeed disappointing not to get a chance to improve my position," said Dwivedi, but added, "In golf you come to accept these situations."
Aman Raj said, "It was quite an experience, but in retrospect, one could have done better, but we learnt a lot."
The 17-year-old Cheng was making his fourth visit to the event.
The second-placed Australian duo -- Ryan Ruffels and Cameron Davis -- were left ruing their missed putts for an eagle and birdie respectively, as that may have helped them tie with Cheng and have a shot at the Masters spot.
When play ended yesterday, Cheng, who led from the first day after his career-best first round of eight-under 62, was 11-under for three rounds, while the Australian duo was at 10-under.
Cheng had rounds of 62, 68 and 69, while Ruffels and Davis carded identical 69, 64 and 67.
At the end of 17 holes in third round, Cheng was 10-under alongside Davis with Ruffels one behind. Cheng and Ruffels birdies, while Davis parred.
Ruffels was looking at and then missed 12-foot eagle putt while Davis missed 12-15 footer for birdie. Meanwhile, Cheng, on the same hole, played a brilliant chip to less than six inches for a tap-in birdie that proved to the winning stroke.
The few holes of play that did take place in the morning for an hour under cloudy skies were a mere aberration as a lengthy suspension in play, due to high winds and rainfall eliminated the possibility of play being completed before darkness.
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