Striker M'Baye Niang controlled the ball ahead of an advancing goalkeeper Wojciech Szczesny before tapping into an empty net.
Niang had been on the sidelines getting treated for an injury and when the ref motioned him to return to the field, he sprinted directly towards the action with Poland's Jan Bednarik completely unaware.
Both the teams have suffered a long wait to qualify for a World Cup tournament as Poland played last at 2006 World Cup, while Senegal played in 2002 World Cup, which was the only World Cup tournament in which it qualified. The Lions of Teranga held on for a 2-1 victory and opened the World Cup with a surprising victory in Moscow.
Cisse said he was proud that all of Africa was rooting for his side though he stressed that the other four African teams, who all lost their opening matches, were not out of it yet.
Mbaye Niang is buried in a green pile by Senegal teammates after scoring the African nation's second goal against Poland.
Senegal was unfancied in the Group H encounter at Otkritie Arena but showed character and took the lead after Thiago Cionek put the ball into his own net.
Senegal were not at their best in the first half, but it was they who did most of the running and looked to make things happen.
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Krychowiak, a midfielder exiled at and then relegated with West Bromwich Albion this season, would reduce the arrears with a header late on but too late.
The 29-year-old is finally reproducing his prolific club form at worldwide level, setting a European qualification record with 16 goals in 10 matches to secure Poland's place in Russian Federation.
Senegal is scheduled to face Japan and Colombia in the next two Group H matches.
Reacting to the win, Cisse who captained Senegal when they stunned France 1-0 in the opening game of the 2002 FIFA World Cup in Korea/Japan, revealed his team secured the win.
Japan's Yuya Osako got the all-important victor in the second half with 17 minutes remaining on the watch, but the South American could not come back as they did in the first half.
Poland enjoyed plenty of the ball in the first half, but Robert Lewandowski was given very little service up front after several promising attacks down the left.
Senegal is making its second World Cup apperance ever.