The match ended 1-1 after extra time with Poland winger Jakub Blaszczykowski putting Poland ahead in the first half before Sheridan Shaqiri's spectacular scissors kick brought the Swiss level in the 82nd minute.
The Swiss hit the bar and forced the Polish goalkeeper into numerous saves as the match wore on but just couldn't convert a chance.
Poland now play the winners of the Croatia-Portugal match in the quarter-finals on Thursday.