Jakub Blaszczykowski, Poland's 30-year-old winger, scored in the 54th minute to give his team the lead.
Although Poland displayed a less-impressive performance compared to their previous two matches, they got the job done with a clean sheet.
Germany, who has beaten Northern Ireland 1-0, topped Group C without conceding a goal.
Northern Ireland will now have to wait for its fate after finishing the group in third place.
Ukraine, on the other hand, said goodbye to the tournament without scoring any goals.