Krychowiak replied with an 86th minute header but it was too little for the Poles who are now in danger of repeating the group stage exit they suffered on their last appearance at the finals in 2006.
The matchup presents a marquee individual showdown between Poland striker Robert Lewandowski and Senegal center back Kalidou Koulibaly.
Finally, his substitutions - introducing Cheikh Ndoye and Kouyate during the second half - were sensible and served to give Senegal more presence and defensive might as Poland sought to find a way back into the game.
Instead, the speedy Mbaye Niang got in front of his defender, nicked the ball away from Szczesny and rolled it into the empty net. "There are no such situations on a daily basis", said Poland defender Michal Pazdan.
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. We didn't create a lot from open play so I think the second game will be different and we can play to our strengths'.More news: England rugby still backing Eddie Jones despite five-Test losing streak
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Nawalka was reluctant to put too much pressure on his star man, Senegal coach Aliou Cisse seemed more relaxed about admitting he is lucky to have a special talent to call on.
Thiago Cionek inadvertently diverted Idrissa Gueye's shot into the net shortly before the half-time break, before a comedy of errors - and a hint of controversy - saw Senegal double their advantage on the hour-mark. The AC Milan forward, who spent the season on loan at Torino, was in two minds whether to shoot or pass, but ended doing neither and the ball fizzled out a goal kick. "We were in possession, I'm convinced they didn't see the player coming off the sidelines", he said.
Szczesny said: 'There is still everything to play for because Colombia, who were the favourites lost their first game so if we get something then everybody is still in the game for the third game.
Poland struggled to respond to falling further behind and as the game entered the final 15 minutes, only Arkadiusz Milik had come close to halving the deficit by missing the near corner from close range.
Despite Krychowiak's late reply, Poland never really looked like snatching a point and must now pick themselves up for the match against Colombia on Sunday.
Poland shifted to a three-man backline at the start of the second half, and Senegal's Salif Sane got a yellow in the 49th for tripping Lewandowski from behind as this forward was running onto a through pass. "We weren't dynamic or co-ordinated".