World number two Wang won the first game convincingly and edged into a 13-10 lead during a captivating second game in Birmingham but the South Korean 2023 champion pegged her back.
Wang scented victory when the scores were tied at 18-18 in the second game but her South Korean opponent took the next three points to level the match.
The decider was also a tight affair but again An, 23, pulled away when the players were level at 18-18, winning her fourth tournament in a row and second at the All England.
Earlier, China's men's world number one Shi delivered a composed performance to see off Taiwan's Lee Chia-hao 21-17, 21-19, also collecting his second All England crown.
Lee, ranked 22nd, was quickly out of the blocks and opened up a three-point lead, but Shi reeled off six straight points to lead 9-6 and never relinquished his advantage.
The tenacious Lee held a 10-9 lead in the second game but he could not pull away from his 29-year-old opponent, who also won the tournament in 2018.
Shi was briefly made to sweat after his 20-16 lead narrowed to 20-19 but he held his nerve to seal victory.
"It's been seven years," said Shi. "A lot has happened during these seven years, ups and downs. I've been to a few semi-finals and didn't make it in the end.
"After these seven years I'm delighted I could win it again.
"It's great that I can pass on some positive energy and values to the fans and in return they offer me support and encouragement."
