Jorgensen needed to beat Indian Srikanth Kidambi to make sure of a place in the last four in Dubai.
And, although Kidambi won the opening game to book his spot in the semis, Jorgensen fought back superbly to come through 17-21 21-12 21-14.
"He needed to win one set [game]; I had to keep doing my best, keep getting every shuttle over the net," Jorgensen said.
"You could see he was a bit slow in the second and third. I'm happy to come through even though I was struggling."
That result means that Japan's Kento Momota makes an early exit despite beating last year's runner-up Tommy Sugiarto 23-21 7-21 21-15, Kidambi progressing from Group B ahead of him by virtue of losing fewer games in the round-robin stage.
The only other match in the men's singles saw Vittinghus overcome Kenichi Tago of Japan 21-19 21-16 to finish second in Group A behind Chen Long.
Meanwhile, in the women's singles Sung Ji-hyun qualified from Group A by cruising to a 21-7 21-11 victory over Wang Shixian, the South Korean going through at the expense of compatriot of Bae Yeon-ju.
Bae threw away a one-game lead as she succumbed to the unbeaten Saina Nehwal of India 15-21 21-7 21-17.
"Bae is the kind of player who will pick up everything. You need to be faster than her to pick up her shots," Nehwal said.
"Under such situations you’re under a lot of pressure. As expected it was a tough fight. The third was a challenge for both of us. Although I was in the semis after winning the second game, I wanted to win the match."
Elsewhere in the draw, Akane Yamaguchi won 19-21 21-14 21-17 to seal top spot in Group B.