Having romped through the opening set, Radwanska looked on course for a straightforward outing against the World No.103. However, it proved to be anything but, the Pole eventually scraping through, 6-2, 6-7(4), 7-5, after saving three match points.
"It was not my best tennis, but I'm very happy that I got the win, and on the important points I was doing a good job, which was the most important thing today," Radwanska said.
"The match points were of course big moments, but also the tie-break in the second set. I came from 4-1 down that set but in the tie-break I didn't play good enough and it slipped away. I was still on court for another hour after that."
Duan, who required a wildcard into the main draw, grabbed her opportunity with both hands, recovering from the loss of the opening four games to gradually overwhelm the World No.3. In the final set it looked like she would claim a famous victory, breaking in the ninth game to serve for the match.
To the disappointment of the upset-hungry crowd, she could not find the finishing blow, three times coming within a point of victory only to be denied each time.
? WTA (@WTA) January 2, 2017
Radwanska made the most of her escape, taking the next two games to book a meeting with Sorana Cirstea.
"It's always tough to play someone for the first time - I didn't know what to expect. But she's a very powerful player and solid from the back," Radwanska said. "She also served very well and had nothing to lose. It was a very close match, even at the beginning."
Elsewhere there were contrasting fortunes for her fellow seeds, Timea Babos and Anastasija Sevastova, both of whom slipped to surprise defeats. Babos failed to make the most of a flying start, losing 1-6, 7-5, 6-2, to Nina Stojanovic, while Sevastova fell to Kristyna Pliskova, 1-6, 6-3, 7-6(6), despite holding a couple of match points in the tie-break.