Sadio Mane teed up Idrissa Gueye on the edge of the box and the Everton midfielder's 25-yard strike took a huge deflection off Thiago Cionek before finding its way into the opposite corner of Wojciech Szczesny's net.
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.
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.
For him the culprits were "a lack of accuracy and quality", "unnecessary mistakes" and failing to match Senegal's "aggression".
Poland responded brightly in the second half as Robert Lewandowski tested Khadim N'Diaye in the 52nd minute, but the Senegal goalkeeper did well to parry his effort away. 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.
If the Polish did not know what a kora or balafon was, they soon found out, because Senegal's support was basically two bands: a gently swaying group with percussion on one side of the pitch, and a high-energy dance troupe with koras, balafons and the kitchen sink on the other.More news: Donald Trump pushes for merit-based immigration system
Poland are the first nation to make two errors leading to a goal in a single World Cup match so far in 2018.
"I'm satisfied with my players, really proud of them".
Krychowiak however pulled a goal back in the 86th minute with a header from Kamil Grosicki's free-kick but Senegal held on.
Poland 0 - Senegal 0. We have had to wait a few days for the eighth segment to get underway, but Tuesday's encounter only served to heighten the sense that this is the most intriguing group of the World Cup.
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.
Lewandowski topped the Bundesliga in scoring in three of the last five seasons and while he had 16 of Poland's 28 goals in qualifying, he managed only one goal at the 2012 European Championship and one at Euro 2016.