With six matches played, Marcello Lippi's defending champions have lost just once so far this campaign - 3-1 at home to Changchun Yatai in March - as they attempt to claim a fourth successive title.
Evergrande were forced to work hard for the first 50 minutes on Friday, as they were twice pegged back by the hosts thanks to goals from Wang Xinxin and Zhou Haibin.
However, two minutes after Tianjin's second in the 52nd minute, Rong Hao put the champions ahead for the third time and Li Weifeng's red card just before the hour mark gave the visitors a further boost.
Elkeson then scored his fifth league goal of the season from the resulting penalty and Gao Lin got his second of the day eight minutes later to wrap up a big win, moving the visitors on to 15 points.
Beijing Guoan kept up the pace with Evergrande thanks to a battling 2-1 victory at Guizhou Renhe on the same day.
With 18 minutes to go, Zhang Chenglin cancelled out Song Boxuan's 56th-minute opener and the two sides looked set to share the spoils, but there was still time for Guoan to snatch all three points.
Pablo Batalla scored his fourth league goal of the campaign in the 80th minute, earning a fifth win from six games for Guoan.
Shandong Luneng and Shanghai SIPG stay just two points behind the leading pair thanks to their respective wins over Hangzhou and Changchun.
Luneng recorded a 2-0 victory against their visitors thanks to their Brazilian double-act in attack, with Aloisio and Vagner Love getting the goals.
SIPG, meanwhile, scored the only goal of their 1-0 victory in the sixth minute - Wang Jiayu with the all-important strike.
Harbin Yiteng's miserable start to life in the Super League continued as they suffered a sixth consecutive loss in the 1-0 defeat by Shanghai Shenxin, while the latter's city rivals Shanghai Shenhua beat Dalian Aerbin 2-0 for only their second win of the season.
Jiangsu Sainty were unable to move to within two points of the top two as they drew 1-1 at home to Liaoning Whowin, with Elias' goal in the 88th minute salvaging a point.
Guangzhou R and F recorded the biggest win of the round, putting four past hapless Henan Jinaye.
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