Aliou Cisse has fielded criticism for being too conservative back in Senegal, but that can not be levelled at him after his approach to this match.
The midfielder's shot appeared to be going wide until the hapless Cionek stuck out a leg and deflected it past Szczesny.
He said they would bring the same focus to their next match against Japan on Sunday, when Poland will play Colombia.
However, it proved too little, too late as Senegal hung on for the famous win, and Africa's first three-point haul at the 2018 World Cup.
Hours after Egypt's loss, Morocco lost 0-1 to Iran at Saint Petersburg in a Group B match, through Aziz Bouhaddouz's own goal in the fifth minute of added time. But like a tiny sliver of light in an otherwise dark tunnel, Senegal defeated Poland, the team ranked eighth in the world.
There was a suggestion Poland had been caught out unfairly for the second goal when Niang came back onto the pitch after he had been at the touchline while Senegal were about to bring on Cheikj Ndoye for Mame Diouf.
But they played with great ambition and goal and showed enough to suggest they could well qualify from what is regarded as a very open group.More news: Hector Cuper rues Mohamed Salah injury after Egypt loss
Senegal have qualified for their second World Cup, after their inaugural participation in 2002 where they reached the quarter-finals.
And their superb post-match celebrations, dancing in the corner in front of their small but jubilant supporters, suggested the tournament will be better for having them in it as long as possible. This team was fast, this team was physical and in Aliou Cisse they had a coach who understands African football and what the World Cup means to Senegal more than anyone else.
Lewandowski was no different against Senegal, landing just one shot on target; a free-kick, which illustrates the lack of service he received.
Group H isn't going how most expected at the 2018 FIFA World Cup in Russian Federation. Kamil Glik was on the bench. He was badly missed.
Senegal take the lead just before half-time!
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.