Sweden international Hysen signed for Shanghai from IFK Goteborg in January and now has four goals in as many matches.
The 32-year-old scored for the third game in a row as his 70th-minute strike helped his side to a 1-0 home win over Beijing Guoan on Friday.
Beijing topped the table going into the match, but had no answer for Hysen's heroics.
Guangzhou Evergrande responded from their first home league loss since July 2012 with a 2-0 win at Jiangsu Sainty.
The AFC Champions League winners secured victory thanks to first-half goals from Elkeson and Rene Junior as they moved back up to second.
Abderrazak Hamdallah scored a hat-trick as Guangzhou R&F beat Hangzhou 6-2 on Sunday.
The match was evenly poised at 2-2 with nine minutes left, but Hamdallah's late treble – and a Lu Lin strike – sealed victory for the hosts, who are now fourth.
Newly promoted Harbin Yiteng saw their struggles continue on Sunday as they lost 3-0 at Tianjin Teda.
Du Zhenyu netted a hat-trick for Tianjin, as Harbin lost their fourth match in a row, leaving them at the foot of the league without a point.
Vagner Love's first-half goal saw Shandong Luneng edge Liaoning Whowin 1-0, while Shanghai Shenxin beat 10-man Guizhou Renhe by the same scoreline.
Dalian Aerbin came from behind to win 2-1 against Changchun Yatai and Shanghai Shenhua and Henan Jianye played out a goalless draw.
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