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 former Arsenal goalkeeper Wojciech Szczesny.
The African side’s second goal arrived on the hour mark, with a touch of controversy. Niang had been off the field for treatment but referee Nawaf Shukralla waved him back on to the field just as Grzegorz Krychowiak lofted a backpass from the centre circle to Szczesny.
Niang intercepted it, knocked the ball past the goalkeeper then sprinted to catch the ball and tapped it into the open net from about eight yards out.
Krychowiak gained some consolation when he headed home a free-kick in the 86th minute but it was too little to late for Poland.
Both teams’ stars, Senegal striker Sadio Mane and Poland forward Robert Lewandowski, rarely threatened in quiet World Cup debuts.
The result means Senegal are joint top of Group H with Japan, who upset Colombia 2-1 earlier in the day. Senegal next play Japan on Sunday afternoon, with Poland meeting Colombia in the evening kick-off.