Marshalled by ex-captain Aliou Cisse, the only black coach at the tournament, Senegal took the lead mere minutes before half-time when Everton midfielder Idrissa Gueye drove a deflected shot in off Thiago Cionek's legs.
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.
Poland have won only one of their seven opening games at the World Cup (D3 L3). Cissé captained the side that progressed so well back in 2002, and also oversaw an undefeated qualification campaign to Russian Federation.
It was the always-dangerous Niang who was at the heart of Senegal's opening goal.
"The scale and size of Robert's talent is vast and it is supported by a lot of hard work", said Nawalka, who has taken his side to eighth in FIFA's world rankings since taking over in 2012.
This will be the first ever encounter between Poland and Senegal.
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Russian police said one of the men was taken to hospital following an incident that saw him cut himself on a carriage door. Tom Law, 29 and Clark Roberts 30, both from Coventry, emerged from the ground singing " Harry Kane , he's one of our own".
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Unlike Lewandowski, Senegal's talisman Mane managed to have a significant effect on the game despite being isolated for long spells. Prior to that they beat South Korea 3-2, but fell to Nigeria 1-0.
Indeed, Lewandowski and co. are at serious risk of a disappointing early exit if they don't recover in their next two games.
With another Polish move breaking down, Krychowiak, who did not cover himself in glory while on loan at West Brom last season, looped a back-pass in the general direction of Southampton's Jan Bednarek, just on as a substitute.
Szczesny rushed out of his area to try and intercept but Niang got to the ball first, slipped it past him and scored into an empty net amid Polish disbelief.
A particular group of fans, painted S-E-N-E-G-A-L colors, were some of the best done-up we've seen so far at this world cup, by far.
Poland kept huffing and puffing and they and Krychowiak gained some consolation when he planted a firm header past Ndiaye with four minutes to play.
Piszczek then failed to hit the target on the volley after connecting with Maciej Rybus' cross from the left on 56 minutes, before a mix-up at the back gifted the Senegalese with a second goal soon afterwards. It's going to count!