Krychowiak replied with an 86th minute header but it was too little for the Poles who are now in danger of repeating the group stage exit they suffered on their last appearance at the finals in 2006.
The Asian team overcame Colombia by the same score earlier in the day.
Poland have won only one of their seven opening games at the World Cup (D3 L3).
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.
But it hardly matters who is officially awarded what; Mane proved his importance by playing a key role in Senegal's attack without really standing out. "We are proud to represent them all", Cisse said.
"I don't know if you get an award for that, Jon, but it's something Federation Internationale de Football Association should look into", he said with full sincerity.
Poland captain Robert Lewandowski was Europe's top scorer in qualifying with 16 goals, but when he stepped up to float a 25-yard free-kick over the wall, Khadim N'Diaye acrobatically dived to turn the ball away. The goalkeeper doesn't know whether to come or not, he eventually decides to but doesn't reach it and Niang races in and taps it into an empty net.
"Of course we represent our country but I can also guarantee that the whole of Africa is supporting us".
"Statistically we had more of the ball but what counts is what ends up in the net".
Here are the name of possible players who can be part of Poland team in today match.
In Monday's pre-match press conference, Senegal coach Aliou Cisse bristled at the suggestion the Liverpool star was not already considered one of the world's best and on Tuesday he helped underline the man-on-Mane narrative by dropping his captain, West Ham's Cheikhou Kouyate, and giving the armband to his superstar.
Arkadiusz Milik hit a first-time effort wide from close range in the 70th minute and four minutes from time, Poland pulled a goal back through Krychowiak as he rose highest to meet Kamil Grosicki's free-kick and power in his header.