Poland came into the game with only one opening-day win at a World Cup finals, which came in the 1974 edition, while Senegal returned after a 16-year absence.
What appeared to work effectively for the Teranga Lions was the pace with which they went about attacking the Polish in the opening exchanges.
Senegal created a good chance on 18 minutes as Mbayiwa Niang got away from his marker to enable a crack at goal, which missed the target as it sailed wide.
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.
Senegal were rewarded for their earlier attempts as a shot down the middle from Issa Gueye deflected off Thiago Cionek and past Woljiech Szcesny on 37 minutes.
Five minutes into the second half, Lewandowski stood tall for a free-kick but Kalidou Ndiaye did well to turn the ball away.
The Teranga Lions made their lead comfortable when a poor back-pass was intercepted by Niang, who eventually ran through into an unguarded goal to tap home the second.
The Polish pulled a goal back four minutes from time through a header from Grzegorz Krychowiak following a free-kick.
However, it proved too little, too late as Senegal hung on for the famous win, and Africa's first three-point haul at the 2018 World Cup.