Neither side's goalkeeper was troubled for much of the 90 minutes but an own goal and a stray back pass handed all the advantage to Senegal, playing in their first World Cup in 16 years, before the Poles secured a late consolation.
After going 2-0 up, Senegal switched to a back five and forced Poland backwards anytime they had the ball by closing them down quickly especially when they approached Senegal's defensive third.
Poland will need to make amends when they take on Colombia - who surprisingly lost to Japan on Tuesday - while Senegal have qualification for the next phase in their sights. Colombia and Poland are both without a point.
The three north African teams - Egypt, Morocco and Iran - had conceded late goals in narrow defeats, while Nigeria were a poor second to Croatia.
Their coach, Aliou Cisse, who captained the team in the country's last World Cup adventure in 2002, said his side because "we were disciplined, compact and aggressive". For him the culprits were "a lack of accuracy and quality", "unnecessary mistakes" and failing to match Senegal's "aggression".
Niang then struck on the hour.
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Striker M'Baye Niang controlled the ball ahead of an advancing goalkeeper Wojciech Szczesny before tapping into an empty net.
Senegal took the lead when Mbaye Niang went around Lukasz Piszczek on the flank following a restart and centred to Sadio Mané.
Don't miss a moment of the World Cup! But the Poland defender Thiago Cionek, near the penalty spot, lifted his right leg and deflected the ball past a wrong-footed Szczesny.
GK Khadim N'Diaye, 7 - Forced to push away a fine Robert Lewandowski free kick at the start of the second - Poland's first effort on target - but was largely untroubled until a series of courageous late claims.
DF Salif Sane, 8 - Troubled by Robert Lewandowski at the start of the second half, picking up a booking, although apart from that he was a rock at the heart of the defence for Senegal, relentlessly protecting N'Diaye's goal.
What neither he nor the dawdling Bednarek spotted was that Niang had just been waved back on the pitch by the referee after some treatment. He was replaced by Bednarek at the start of the second half.