In a tightly-fought contest, Thiago Cionek's unfortunate own goal (37) handed Senegal the lead before their advantage was doubled through M'Baye Niang (60), who capitalised on a poor backpass from Grzegorz Krychowiak to score his first global goal.
Niang had been on the sidelines getting treated for an injury and when the ref motioned him to return to the field, he sprinted directly towards the action with Poland's Jan Bednarik completely unaware.
The coach of Poland, Adam Nawalka, was "surprised" at the circumstances that led to Senegal's decisive second goal in Wednesday's Group H clash.
The goal made a huge difference in the match, as Poland later scored on a header to bring it to 2-1.
Coach Aliou Cisse is proud of his players while claiming the whole of Africa is rooting for Senegal.
If Senegal wanted a leader at the back, it was Koulibaly, who dominated his defensive line with total confidence. It's a speedy, confident side and they proved on Tuesday that it can make even more noise in this tourney.
Poland will need to turn things around when it takes on Colombia - which surprisingly lost to Japan on Tuesday - while Senegal has qualification for the next phase in its sights.
The 29-year-old is finally reproducing his prolific club form at global level, setting a European qualification record with 16 goals in 10 matches to secure Poland's place in Russian Federation.
He was not overly happy with Niang's goal, either, as the Torino striker had been off receiving treatment but was waved on by the referee just as Krychowiak played a bouncing back pass towards Bednarek. I get phone calls from everywhere.
The Asian team overcame Colombia by the same score earlier in the day. His face appears on stamps back in his homeland, and he will be looking to shine on his World Cup debut in Moscow's Spartak Stadium.