Wang Helong's men have lost all five of their opening matches in their first top-flight campaign, and must stop that run quickly to avoid getting cut adrift at the bottom of the table.
They face the side directly above them this weekend and could fall six points behind if Shenxin claim victory.
Henan Jianye, who were promoted alongside Harbin, have fared better in their start to life back at the top level and collected their first win of the season against Shanghai SIPG last weekend.
They travel to Guangzhou R and F on Sunday, and could go above their opponents if they can inflict their first home defeat of the season.
Top two Guangzhou Evergrande and Beijing Guoan both face away trips, with Marcello Lippi's defending champions travelling to struggling Tianjin Teda on Friday looking to boost their already impressive goal difference.
After the opening five matches of the season, Evergrande have scored 14 goals and their plus-eight goal difference is the reason they currently occupy top spot.
Beijing's success has been built on defence, and having only conceded once so far they will hope to record a fifth win of the campaign when they face mid-table Guizhou Renhe the same day.
After a strong start, a switch in focus to AFC Champions League action has brought a blip for Lei Gong's side domestically, and Guizhou will not want to slip to a third consecutive league defeat.
Jiangsu Sainty, who moved into the top three with victory over Shandong Luneng on Wednesday, host Liaoning Whowin hoping to take advantage of any slip-ups from the top two.
Meanwhile, Shandong host Hangzhou, Changchun Yatai travel to Shanghai SIPG and strugglers Shanghai Shenhua will look to end a run of four games without a win against Dalian Aerbin.
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