The leader from round one, the 25-year-old Jang had started the day five shots ahead of playing partner Annika Sorenstam and American Cristie Kerr, and never looked like faltering.
She finished on 16 under par and was a four shot winner over Gustafson, the Swede who won the championship when it was last played at Birkdale five years ago and made her final day move with a 67.
Michelle Wie, the phenomenal 15-year-old American amateur, and South Korea's Kim Young closed with rounds of 69 to share third place on 10 under.
Sorenstam, seeking a third major and a seventh win of her outstanding season, never got closer than four shots and her hoped for 10th career major and second British Open title started to unravel when she took two in a greenside bunker and dropped a shot at the 16th.
Worse followed at the par five last where she lost her ball from the tee and took a double-bogey seven for a 71 and slipped back into a tie for fifth on nine under.
For Wie, it was another outstanding effort. She has played in eight majors, and this was her fourth top 10.
This season, she finished tied for 14th at the Kraft Nabisco Championship, second to Sorenstam at the McDonald's LPGA Championship and joint 23rd in the US Women's Open.
Kent's Karen Stupples put up a stout defence, closing with a 71 to tie for 11th on seven under. She was the leading British player, one ahead of Wales Becky Morgan, who shot 70.
For Jang - known as JJ -it was a first win in six seasons on the LPGA Tour and she became the second Korean to win the British Open, following in the footsteps of the 2001 champion and four-time major winner Se Ri Pak.
Grace Park, in last year's Kraft Nabisco, and Birdie Kim, in last month's US Women's Open, are the other from her country to land majors.
Jang had never won in six seasons on the LPGA Tour, but had come close on many occasions and was regarded by many of her peers as the best player still waiting to make the victory breakthrough.
And she shrugged off any notion that she might be intimidated by playing alongside Sorenstam. The Swede never got closer than four shots and it was Gustafson who made the biggest surge.
She got to within two shots with three to play but, crucially, could not make birdies at the relatively easy par five 17th or 18th.
For Jang, it really was an overdue win. She has had three seconds and 30 top 10s since joining the LPGA in 2000 and she added the ï¿½160,000 first prize to her career earnings of more than ï¿½1.2million.
"I feel great," she said. "My first win and my first major. I feel very lucky."
Sorenstam was generous in defeat. "JJ played incredibly and would have been very hard to catch today so hats off to her. "I was pretty happy with the way I played but just didn't finish well."
Women's British Open (Royal Birkdale), leading final round scores: 272 Jang Jeong (S Kor) 68 66 69 69; 276 S Gustafson (Swe) 69 73 67 67; 278 Young Kim (S Kor) 74 68 67 69; *M Wie (US) 75 67 67 69 279 L Neumann (Swe) 71 70 68 70; C Kerr (US) 73 66 69 71; A Sorenstam (Swe) 73 69 66 71.
*denotes amateurReuse content