Later, a resurgent Mark Philippoussis pummelled Argentine Federico Browne 6-4, 6-3 under the floodlights to reach the last 16 of the $860,000 event in Tokyo.
A quarterfinalist in his hometown Bangkok last week, Paradorn dug himself out of a hole at a set and 2-0 down in the second.
The third seed finally broke back in the eighth game before taking the tie-break 7-3 with a ferocious backhand pass.
Broken by Norman in the eighth game of the final set, Paradorn produced a string of superb shots to hit back in the very next game.
"I was down 5-3 and he was serving for the match and 30-15. It was almost done," said the 24 year-old Thai, chasing a third ATP tour title of the year.
"Either I break back or I'm finished, so I played my best game and just tried to get back into the match and force another tie-break."
A fist-pumping Paradorn quickly seized control after that and went on to take the third-set tie-break 7-2, wrapping up victory in two hours and 11 minutes.
Wimbledon runner-up Philippoussis, who ended a two-year title drought with victory in Shanghai at the weekend, took just over an hour to dispatch Browne on centre court.
Earlier, second seed Sebastien Grosjean won his first match since August with a businesslike 6-3, 7-6 success over towering Croat Ivo Karlovic.
The Frenchman, counterpunching effectively against his 2.08m opponent, took the first set comfortably and prevailed 10-8 in a high-quality second-set tie-break.
World number 10 Grosjean, who had not won a match since a second-round victory at the Tennis Masters Series in Montreal, plays Dutchman Dennis van Scheppingen in the third round.
Fourth seeded Czech Jiri Novak beat German Bjorn Phau 7-6, 6-2 while ninth seed Kenneth Carlsen also advanced, the Dane overpowering Goichi Motomura 6-2, 7-6.
But Takao Suzuki, who has just got engaged, gained a measure of revenge for Japan, ousting fourteenth seeded South African Wesley Moodie 6-1, 7-6 behind a sharp serve-and-volley game. Suzuki plays Paradorn next.
In the women's draw, top seeded Ai Sugiyama squandered three match points before finally putting away a determined Yuka Yoshida 6-3, 3-6, 7-6 in a tense all-Japanese affair.
Sugiyama, Japan Open champion in 1997 and 1998, next plays Aniko Kapros after the Hungarian thrashed Switzerland's Emmanuelle Gagliardi 6-0, 6-2.
