West Bromwich Albion midfielder Grzegorz Krychowiak got Poland back in the game with an 86th-minute header but Senegal hung on at Moscow's Spartak Stadium.
After Niang doubled the lead in the 60th, Krychowiak headed in Kamil Grosicki's free kick in the 86th minute, ending a streak of five straight scoreless openers for Poland.
Senegal coach Aliou Cisse refused to accept their 2-1 win over Poland on Tuesday was all down to errors by their opponents, saying discipline and faith in themselves as a new generation of African talent were key.
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. From there, in what was its first and until now only World Cup, Senegal went on a run to the quarterfinals.
Goal scorer Mbaye Niang said: "We deserved our luck because we worked really hard". It's a speedy, confident side and they proved on Tuesday that it can make even more noise in this tourney. Both Senegal and Poland are playing with attacking mindset and not shying away from pressing deeper. "There were lots of unnecessary mistakes and lack of accuracy, and simply we didn't play a very fluid football".
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Niang pounced on a poor backpass from Krychowiak and capitalised on hesitation between Szczesny and Jan Bednarek to nip in and slot into an open net on the hour mark. Senegal will play Japan on Sunday, when Poland meets Colombia.
"The first half was much worse than the second, we played better after the break but it wasn't enough".
Cisse said he was proud that all of Africa was rooting for his side though he stressed that the other four African teams, who all lost their opening matches, were not out of it yet.
The contest had been set up as a battle between two players who occupy the tier of talent just below the holy trinity of Messi, Neymar and Ronaldo: Poland's captain and talisman Robert Lewandowski and Senegal's main man, Sadio Mane. He tees up Gueye who rifles a low shot from the top of the box, it takes a wicked deflection off Cionek, wrong-footing the goalkeeper and ending up in the back of the net. A few hours after Senegal's win, Egypt then also lost its second match, 3-1, against Russian Federation.