While Grzegorz Krychowiak pulled a goal back for Poland in the closing minutes, they were unable to find a second to rescue a point.
M'Baye Niang sprinted back on to the field of play after injury and immediately intercepted a backpass from midfield, beating former Arsenal goalkeeper Wojciech Szczesny and Southampton defender Jan Bednarek to the ball.
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. "I felt there was something on and was able to get in there and score".
"He is a unique player and he can not be compared to any other Senegal player, even the major ones we've had in the past", said Cisse.
Grzegorz Krychowiak, author of the wayward back pass, made partial amends with a header five minutes from time but it was too late.
"OK, it's important to get off to a good start but the second and third matches are important as well, so hopefully Egypt, Morocco, Tunisia and Nigeria will step up".
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Mbaye Niang is buried in a green pile by Senegal teammates after scoring the African nation's second goal against Poland.
Senegal's coach Aliou Cisse thanks the crowd after his team's victory on Tuesday night. We were able to put them under pressure.
"I can tell you that the whole of Africa was supporting us, and they are still doing so".
The first half hour was a sorry affair strewn with misplaced passes from both sides and neither of the danger men, Lewandowski and Senegal's Sadio Mane, saw much of the ball. "That's not how we take points", the Poland captain said, via L'Equipe.
Senegal took the lead when Niang went around Lukasz Piszczek on the flank following a restart and centred to Mane.
Senegal were rewarded for their earlier attempts as a shot down the middle from Issa Gueye deflected off Thiago Cionek and past Woljiech Szcesny on 37 minutes. That's when you need your best players to produce small moments to edge the contest, and Mane subtly stepped up.