Shanghai's hope of leveling the game was shattered as Barbra Banda's shot in the 87th minute hit the woodwork and bounced off.
Fiorentina loanee Pedro put the hosts ahead with a low strike before Bruno Henrique converted from the penalty spot after a Leo Gomes handball.
Saturday ended with Newcastle United winning 3-1 at home to Burnley thanks to an excellent display from winger Allan Saint-Maximin. The Frenchman scored his side's first goal and then set up Callum Wilson for Newcastle's second of the game just four minutes after Ashley Westwood's 61st minute equalizer for the visitors.
Four naturalized players Jiang Guangtai, Fei Nanduo, Ai Kesen and Li Ke were called up. Wu Xinghan from Shandong Luneng replaced Wuhan Zall midfielder Liu Yun who misses out due to injury.
Having overcome last season's top-ranked side Beijing on Thursday, Jiangsu never looked threatened from the tip-off on Monday. They out-rebounded Tianjin 43-25 to score 26 points on second chances.
"Schalke's squad is poorly composed. We are talking about the sins of the past," the 59-year-old said.
Han Ziqi contributed a game-high 23 points, but her solo effort could not save Tianjin from a big loss.
With a perfect record in the new season, Jiangsu expects a tough route ahead as title contender Xinjiang awaits them on Saturday.
Ben Chilwell had a perfect Chelsea debut with the opening goal and an assist for Kurt Zouma in Chelsea's 4-0 win at home over Crystal Palace, which was rounded off by two penalties from Jorginho.
Leeds United and Manchester City produced a game that lived up to expectations in terms of entertainment with the teams taking one point each after a 1-1 draw.
However, Bayern had the last laugh in the closing period after Maximilian Mittelstadt felled Lewandowski inside the box to concede a penalty. The Poland international stepped up and kept his nerves after beating Alexander Schwolow into the bottom left corner.