Jia Xiuquan's men came into the clash having won just once in their previous eight league outings, but it looked as though they would arrest that slump as they led 2-1 heading into stoppage time.
However, Han Deming, who had earlier given hosts Harbin the lead in the 39th minute, struck an injury-time leveller to ensure both sides took a point.
Zhang Lu's effort a minute into the second half put Henan on level terms following Harbin's opener.
Dori's own goal then looked as though it would prove decisive, until Han struck late on to break Henan hearts.
Liaoning Whowin's 3-0 victory over Shanghai Shenxin on Sunday ensured Henan dropped into the bottom two.
At the opposite end of the table, Guangzhou Evergrande's inexorable march towards the title continued as they brushed aside Shanghai SIPG 3-0 away from home.
Marcello Lippi's men hit the front in the seventh minute through Gao Lin, before a second-half brace from Elkeson - who now boasts 22 goals this season - sealed the points.
Beijing Guoan are six points behind the defending champions after twice coming from behind to record a 3-2 win at Jiangsu Sainty.
Liu Jianye gave Jiangsu the advantage midway through the first half, only for Xu Yunlong to level in the 37th minute.
Roda Antar's penalty restored the home side's lead, but two goals in 11 second-half minutes from Dejan Damjanovic and Zhang Xizhe ensured Beijing did not lose any ground on the leaders.
Guangzhou R&F took advantage of SIPG's defeat in the race for an AFC Champions League berth, running out comfortable 4-0 winners at home to Shanghai Shenhua.
Shandong Luneng's margin of victory was much more narrow as Aloisio's goal earned a 1-0 success over Changchun Yatai, while there were also wins for Hangzhou and Dalian Aerbin.
Hangzhou saw off Tianjin Teda 2-1 thanks to a brace from Davy Angan, while Dalian were grateful to two late goals from Bruno Meneghel for their 2-0 triumph at Guizhou Renhe.
