Xiao Zhi scored the winner 15 minutes from time with a header that went in off the inside of the post after R&F's Eran Zahavi and Alan Carvalho of Evergrande had both claimed hat-tricks.
Zahavi struck twice from outside the area in the opening 10 minutes before Carvalho ensured the champions went into the break in front with three goals in a 32-minute spell before the interval.
Former Israel international Zahavi, the Chinese Super League's top scorer last season, restored parity just four minutes after the restart before Junior Urso put R&F in front when goalkeeper Liu Dianzuo fumbled his long-range attempt.
A penalty from Ricardo Goulart levelled the scores yet again only for Xiao's header to seal all three points for Dragan Stojkovic's side.
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"This game is not about our forwards, I should have prepared my defenders better," said new Evergrande coach Fabio Cannavaro.
"Our defenders are the best we have and I don't want to see what happened today happening again. We have to face the problem.
"We will meet lots of top strikers later and we have to come up with an integrated defence, not confronting players individually."
Elsewhere, Tianjin Quanjian began the new season with a 4-0 thrashing of Henan Jianye, with both Anthony Modeste scoring twice and Axel Witsel also on the scoresheet while Shanghai Shenhua were held to a 1-1 draw by Changchun Yatai.
(This version of the story repeats to change headline, no change in text.)
(Reporting by Michael Church, editing by Pritha Sarkar)
