An own goal from Thiago Cionek and a second-half effort from M'Baye Niang gave Senegal a two-goal lead and although Grzegorz Krychowiak halved the deficit late on, Aliou Cisse's team were full value for the three points.
After Japan had registered a surprise 2-1 victory over Colombia earlier on Tuesday, both teams were aware that Group H was wide open but neither side showed much ambition during the opening stages of the contest.
The first chance came in the 18th minute after Niang had been played through on goal, but the striker dragged a left-footed shot well wide of the far post.
Up the other end, a scuffed shot led to Kamil Grosicki directing a header towards the top corner, but his improvised attempt went over the crossbar.
The middle period of the first half passed by without incident with time in possession the priority but shortly before the break, Senegal made the breakthrough that they and the game required.
Sadio Mane teed up Idrissa Gueye on the edge of the box and the Everton midfielder's 25-yard strike took a huge deflection off Cionek before finding its way into the opposite corner of Wojciech Szczesny's net.
Senegal could have made it two soon afterwards but Salif Sane headed over the crossbar from 12 yards out after meeting an outswinging corner from the right.
Poland improved after the restart with Robert Lewandowski seeing a 25-yard free kick punched clear by Khadim N'Diaye, but Senegal were not prepared to sit back with Mane becoming increasing involved in the final third.
Their approach paid off just after the hour mark but Poland contributed to their own downfall as 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.
Niang had just returned to the pitch after consulting tactics with the coaching staff but the forward capitalised by getting between the two Poland players, flicking the ball towards goal and tapping into the net from close range.
Poland struggled to respond to falling further behind and as the game entered the final 15 minutes, only Arkadiusz Milik had come close to halving the deficit by missing the near corner from close range.
Dawid Kownacki also sent a header too close to N'Diaye as the match edged closer to full time but with four minutes left, Poland finally got themselves back into the contest through Krychowiak, who powered a header into the far corner after meeting a deep set piece.
Poland continued to launch the ball into the penalty area during four minutes of added-on time, but Senegal successfully repelled the danger to start just their second-ever appearance in this tournament with a win.
POLAND (4-3-3): Szczesny; Piszczek (Bereszynski 83'), Pazdan, Cionek, Rybus; Blaszczykowski (Bednarek 46'), Krychowiak, Zielinski; Grosicki, Milik (Kownacki 73'), Lewandowski
SENEGAL (4-2-3-1): K N'Diaye; Sabaly, Koulibaly, Sane, Wague; Gueye, A N'Diaye (Kouyate 87'); Diouf (N'Doye 62'), Mane, Sarr; Niang (Konate 75')