The point left Fabio Cannavaro's side on 22 from 11 matches, alongside Beijing Guoan, Shanghai SIPG and Shandong Luneng, after former Valencia midfielder Michel Herrero converted an 86th spot kick for Guangzhou R&F at Tianhe Stadium.
The Spaniard had clipped the visitors into a 39th minute lead after being sent clear but the four-times defending champions stormed back with a two-goal, five minute salvo.
R&F's Chinese international Jiang Zhipeng gave away a penalty in the 74th minute after he fell on the ball and handled as he attempted to deal with a long pass from deep.
Gao Lin stepped up and confidently sent the goalkeeper the wrong way from the spot before a sweeping counter attack was finished off expertly by Ricardo Goulart, who nodded in for his ninth of the campaign.
However, the hosts could not hold on.
R&F were eventually given a late penalty after numerous previous appeals, including one comical dive by Nigerian striker Aaron Samuel that led to a booking, when Tang Miao was felled in the box. Michel followed Gao by sending the keeper the wrong way.
Evergrande are top on goal difference ahead of Shandong Luneng who beat visitors Shanghai Shenhua 2-0 on Saturday. Beijing Guoan are fourth after a goalless draw at sixth-placed Jiangsu Sainty, who are level on 16 points with R&F.
Evergrande and Beijing failed to capitalise on early season pacesetters Shanghai SIPG suffering their first defeat of the season at Guizhou Renhe, who moved out of the relegation zone with a surprise 2-0 home win on Friday.