Saina Nehwal and Kidambi Srikanth also won their respective matches to make it to the last-eight stage.
But it was Prannoy's high-voltage encounter that saw some spectacular strokes, a contentious line call and India coach Pullela Gopichand losing his cool, even as the 22-year-old player came out with flying colours with a 18-21 21-14 21-14 win over the All England finalist at the Siri Fort Sports Complex.
Later in the day, Srikanth saw off Japan's Kento Momota 21-12 15-21 21-15, while RMV Gurusaidutt prevailed over young Sameer Verma 18-21 21-19 21-18 in a hour's match.
Among other Indians in fray, Commonwealth games champion Parupalli Kashyap paid for his series of errors as he went down 17-21 11-21 to China's Xue Song in another pre-quarters match.
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However, in the second game, the Indian fought back from 4-7 down to slowly distance himself for the German Open winner and eventually bounced back into the contest when the Dane hit wide.
With the crowd vociferously rooting for him, Prannoy changed his tactics in the decider. He caught hold the shuttles early and rode on his accurate strokeplay to lead 9-3 at one stage. Jorgensen, however, fought back to narrow the gap to 9-11 at the break.
Prannoy immediately requested for a referral but he was denied by the chair umpire, who overruled the decision and awarded the point to Jorgensen.