Nawalka sent on Southampton defender Jan Bednarek at half-time - Jakub Blaszczykowski making way on his 100th worldwide appearance - as Cionek's own goal ensured Poland's 32-year wait for a clean sheet at the World Cup goes on.
Senegal defeated Group H favourites Poland 2-1 at the World Cup on Tuesday thanks to an own goal and and a controversial second strike.
Poland have won only one of their seven opening games at the World Cup (D3 L3).
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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.
Their approach paid off just after the hour mark but Poland contributed to their own downfall as Grzegorz Krychowiak's back-pass from the halfway line was short, leading to confusion between Jan Bednarek and Szczesny who failed to make connection with the ball. Poland is a good bet to score at least one, as is Senegal and its potent attack.
Arkadiusz Milik hit a first-time effort wide from close range in the 70th minute and four minutes from time, Poland pulled a goal back through Krychowiak as he rose highest to meet Kamil Grosicki's free-kick and power in his header.
The goal sparked wild celebrations among the Senegalese players and incredulity among Poland's.
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Poland appeared to be coming back into the game until the most embarrassing moment of the World Cup so far.
This is Senegal's second appearance at the World Cup and it's the second time the team has come away with a monumental win.
Lewandowski curled the free kick over the Senegal wall but Khadim Ndiaye - the only African-based player in Senegal's squad - pushed it away.
Niang was a constant threat to Poland's backline as he caused Lukasz Piszczek and Cionek plenty of problems on the left side.
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After a tight first half hour, it was the always-threatening Niang who was at the heart of Senegal's opening goal.