In a match billed as a straight fight between super-strikers Robert Lewandowski and Sadio Mane, neither scored but Liverpool striker Mane set up Idrissa Gueye for the shot that took a wicked deflection off Cionek, leaving Szczesny totally wrong-footed in the Polish goal for Senegal's opener on 37 minutes.
On the same Japan shocked Colombia, Senegal pulled off a similar surprise against the No. 8 FIFA-ranked Poland, coming away with a 2-1 victory that was also controversial.
Niang, who had returned to the field from treatment, later beat Szczesny to a backpass and had an open net when he doubled the lead in the 60th.
Senegal beat Poland 2-1 in their first Group H match.
Where is FIFA World Cup 2018 Poland vs Senegal match being played? After going 2-0 up, Senegal switched to a back five and forced Poland backwards anytime they had the ball by closing them down quickly especially when they approached Senegal's defensive third. Colombia and Poland are both without a point.
On Wednesday, Morocco too will be facing Portugal in a Group B match at the Luzhniki Stadium in Moscow needing a win to stay on.
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Robert Lewandowski of Poland (right) is consoled by his wife Anna after losing against Senegal on Tuesday night.
He sparked numerous Senegal attacks and capped off an impressive performance with a goal on the hour-mark.
Poland got a goal back with Krychowiak's header in the 86th minute, and though they pushed forward for an equaliser, a second goal would not come late on.
"We are Senegal, so we are proud to play for our country but I can see that the whole continent is supporting us, too".
Poland didn't look likely to find a way back into the game at 1-0, but Szczesny's costly error made things all the more hard for his side.
Senegal's forward Mbaye Niang (R) celebrates after scoring their second goal during the Russian Federation 2018 World Cup Group H football match between Poland and Senegal at the Spartak Stadium in Moscow on June 19, 2018.