Parnevik shot a two-under-par 70 to finish the six-day, four-nation event on 276, four shots ahead of his English rival.
"I did not know what to expect coming into the final round," said the Swede.
"I had a cough and fever when I arrived last night, but I managed to get off to a good start with birdies at one and three.
"Nick was struggling with his putting on the front nine. He improved on the back nine, but by then it was a little too late."
Three-times Open champion Faldo also compiled a 70 in the final round to take second place by two shots from Thailand's Boonchu Ruangkit. The defending champion, Ernie Els of South Africa, came fourth on 283.
This year's Super Tour teed off in Jakarta and went through Bangkok and Boracay before winding up in Taiwan.
In Hong Kong, Scotland's Kenny Walker succumbed to nerves on the final day of the PGA Championship. The overnight leader slumped to a 73 to finish joint fourth on 274, six under par and four shots behind Filipino Rodrigo Cuello, who won with a four-under final round of 66.
Walker, who had played steadily for the first three rounds, said: "I was very nervous. I'm not really used to such pressure."