Kashyap, who had reached the quarterfinals stage in London Olympics, won 24-22 20-22 22-20 in a marathon opening round match that lasted an hour and eight minutes.
Olympics bronze medallist Saina Nehwal also opened her campaign on a positive note, prevailing over Aprilla Yuswandari of Indonesia in straight games to reach the second round of women's singles event.
World number three Saina took time to get into the groove but went from strength to strength as the match progressed to notch up a 22-20 21-8 win over Aprilla at the Hong Kong Coliseum at Kowloon.
Ajay Jayaram also reached the second round after seeing off Zhengming Wang of China 22-20 23-21 in another men's singles match.
Kashyap showed tremendous resilience and a never-say-die attitude and matched Jorgensen with his repertoire of strokes during the thrilling match.
Trailing 0-3 initially, Kashyap turned the tables on Jorgensen and moved into the break at 11-8. The Dane, however, clawed back 13-13, but the Indian fought tooth and nail to nose ahead.
In the second game, Jorgensen and Kashyap traded points right from the start but it was the Dane who had enjoyed the lead most of the time and eventually succeeded to staving off the challenge from the Indian to bounce back into the contest.
The decider turned out to be a cliff-hanger as Kashyap showed nerves of steel and didn't let go off opportunities and despite being pushed to a 2-5 deficit early on, wrestled his way to lead 11-10 at the break.
After the breather, Kashyap slowly widened the gap and moved to 19-15. Jorgensen clawed back to 20-20 but it was the 26-year-old Indian who had the last laugh. MORE
