Austrian Ofner looked destined for the next round when he surged to a commanding 6-1 lead in the deciding set tiebreak against 20-year-old American Basavareddy.
But after winning another point to move 7-1 ahead, Ofner began celebrating and walked confidently toward the net - apparently forgetting that final-set tiebreaks require 10 points to win and not the usual seven.
The sheepish realisation of his blunder was written all over Ofner's face as he trudged back to the baseline, but the damage was already done as Basavareddy had all the motivation he needed.
What followed was a dramatic turnaround as Basavareddy reeled off eight of the next nine points before snatching a stunning 4-6 6-4 7-6 (11) victory from the jaws of defeat.
Basavareddy marked his remarkable comeback by first holding his hands at his neck in a 'choking' celebration before pumping his fist, while a deflated Ofner could only shake hands and contemplate what might have been.
The victory was particularly sweet for the American, who earned his stripes as a wildcard last year when he took the opening set off 10-times champion Novak Djokovic in the first round before eventually being eliminated.