Szczesney came rushing out to collect a wayward back-pass but completely mistimed his run and failed to clear the ball, allowing Niang to tap into an open goal for Senegal's all-important second goal.
However, Cisse's men held on to record something of a surprise opening win.
The Southampton defender did not see the Senegalese poacher until it was too late and he then poked the ball past Szczesny's late-arriving cavalry and walked the ball into the net.
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They were unable to get the equalizer, however, and Senegal took the match 2-1.
Krychowiak headed Poland's goal in the 86th minute. Lewandowski admits he has a point to prove after a disappointing Euro 2016, when he scored only once as Poland exited at the quarter-finals stage.
Despite being, arguably, the best African team at the 2018 World Cup-led by star players like Sadio Mané, Kalidou Koulibaly, and Cheikhou Kouyaté-they were widely considered to be underdogs against Robert Lewandowski's Poland.
The seeded team in the group, Poland had been hoping to inflict a fifth straight defeat on Russian Federation 2018's African contingent but they did not account for their opponents' tactical discipline or good fortune.
Well-marshalled by Senegal's imposing central defenders, Lewandowski could not get a sniff, while Mane spent the first 25 minutes on the left touchline, just where Poland wanted him.
Krychowiak needlessly hooked a high ball back towards his own goal from inside the Senegal half and with Szczesny attempting to intercept by coming out of his penalty area, Niang gleefully knocked the ball into an unguarded goal. The scoreline reads 0-0 but Senegal have had more opportunities going forward and have looked the more comfortable side on the game so far.
"I'm satisfied with my players, really proud of them".