Senegal, back in the tournament for the first time since 2002, went ahead in the 37th minute when Thiago Cionek's attempted block of Idrissa Gueye's shot wrong-footed goalkeeper Wojciech Szczesny, who was picked to start over fellow Arsenal castoff Lukasz Fabianski.
However, Cisse's men held on to record something of a surprise opening win.
After Japan's 2-1 victory over Colombia earlier on Tuesday the group remains open but Poland will need to show a dramatic improvement when they face the South Americans next. The goalkeeper doesn't know whether to come or not, he eventually decides to but doesn't reach it and Niang races in and taps it into an empty net.More news: A 'milestone' World Cup win kicks off celebration for Mexico
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.
Senegal's players celebrate their win over Poland. Poland meets Colombia the same day in what could be an unofficial elimination game because a second loss could prove costly in Group H. Both matches can be streamed on fuboTV (Try for free).
A rare sight on goal for Poland fell to Robert Lewandowski, but the best he could do was a shot into the ground following a turn on the edge of the box.
Well-marshalled by Senegal's imposing central defenders, Lewandowski could not get a sniff, while Mane spent the first 25 minutes on the left touchline, just where Poland wanted him. Having watched all of their African rivals lose their opening group games, Senegal started on the front-foot and deserved their huge slice of luck.More news: M’Baye Niang pounces to secure Senegal victory after Poland mix-up
The first half hour was a sorry affair strewn with misplaced passes from both sides and neither of the dangermen, Lewandowski and Senegal's Sadio Mane, seeing much of the ball.
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.
It was a particularly disappointing display after an impressive qualifying campaign that helped lift Poland to eighth in the world rankings and brought them to their first World Cup for 12 years with high hopes.
Senegal's forward Mbaye Niang (R) celebrates after scoring their second goal during the Russian Federation 2018 World Cup Group H football match between Poland and Senegal at the Spartak Stadium in Moscow on June 19, 2018.More news: China 'underestimated' Trump, a key adviser says