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Feng, the first player from mainland China to win a major championship when she won the LPGA Championship in June, had six birdies at the Emirates Golf Club.
"I was patient because I was only 1 under after seven holes," Feng said. "I missed a lot of chances but then made a 15-footer on 8 and started doing really well from there."
Parker moved into a tie for the lead by birdieing the par-5 18th.
"My putting was really good today," the Englishwoman said. "I hit 14 greens, had 26 putts, so I rolled them in nicely and got off to a good start. I've always done well on this course."
American Cindy Lacrosse, the Czech Republic's Klara Spilkova and Wales' Sahra Hassan were a stroke behind in the Ladies European Tour's season-ending event.
Lexi Thompson, the American who won the event last year at age 16, opened with a 69.
"I could have dropped a few more putts. I had a lot of lip-outs out there. But I'll take 3 under for a first round," said Thompson, who had two bogeys on her first four holes. "If I can stay around there and shoot a few more under than that, I'll be in a good position."
Michelle Wie was four shots back after a 70. Spain's Carlota Ciganda, the LET money leader, also opened with a 70.