In a tightly-fought contest, Thiago Cionek's unfortunate own goal handed Senegal the lead before their advantage was doubled through M'Baye Niang who capitalized on a poor back pass from Grzegorz Krychowiak to score his first international goal after running on from the sideline having received treatment.
Krychowiak pulled a goal back for Poland with a powerful header four minutes from time, but Senegal held on for victory. Senegal were making their first appearance in the tournament since 2002.
Meanwhile, hosts Russia secured a 3-1 win over Egypt in St Petersburg to put themselves on the brink of advancing to the round of sixteen.
Ahmed Fathi's own goal broke the deadlock, before Denis Cheryshev and Artem Dzyuba struck twice in three minutes to settle the Group A clash and move Russia to six points after two games.
Mo Salah, who was included from the start, pulled a goal back from the spot with 17 minutes left, but it will take an unlikely scenario to prevent the hosts from progressing while Egypt's tournament is all but over after two straight defeats.
Their final match will be against Saudi Arabia who are due to play Uruguay today at 6pm.