The opener from Giroud saw the centre-forward become France's highest goalscorer of all time, with the 36-year-old, who has benefited from Karim Benzema's absence at the tournament, moving past Thierry Henry.
Mbappe then doubled France's advantage in the 74th minute before scoring again late on, with the Paris Saint-Germain attacker producing another standout performance for Didier Deschamps's side at the tournament.
Robert Lewandowski found the back of the net from the penalty spot in the final exchanges, but it only proved to be a consolation for Poland.
The reigning champions will take on either England or Senegal in the quarter-finals of the competition on December 10.
France had a half-chance in the fourth minute when Raphael Varane climbed highest inside the penalty box to meet a corner, but the centre-back's header was over the crossbar.
Poland were struggling to get out of their own half in the early exchanges, with Mbappe's pace causing all sorts of problems in a wide area, and the crowd came alive whenever he took possession of the ball.
Wojciech Szczesny had to get down to keep out a powerful strike from Aurelien Tchouameni in the 13th minute, before the Poland goalkeeper denied Ousmane Dembele.
Szczesny then denied Antoine Griezmann from close range before Lewandowski fired one wide of Hugo Lloris's post down the other end of the field.
France had another excellent chance in the 29th minute when Dembele found space down the right before delivering a low cross into the Poland box, but Giroud somehow missed the post.
The White-Reds were causing problems down the other end, with Matty Cash firing wide of the post, but the main danger was coming from Mbappe, who hit the side-netting in the 35th minute.
Poland had a golden chance late in the first period when Piotr Zielinski found space inside the box, but his first effort was saved by Lloris before his second was blocked by Dayot Upamecano.
France made the breakthrough in the 44th minute of the contest when Giroud collected a pass from Mbappe before finding the bottom corner of the net to become his country's all-time leading goalscorer.
Zielinski almost answered back before the interval, with the midfielder having a shot blocked into the side-netting, but Giroud's goal separated the two sides at the interval.
Mbappe had one deflected just wide of the Poland post in the 57th minute, before Giroud had a spectacular goal disallowed following an injury to Szczesny, who stayed down following a collision with Varane.
Kamil Glik headed over the France crossbar in the 72nd minute, but the match was taken away from Poland in the 75th minute when Mbappe fired one into the back of the net with a thunderous effort.
Theo Hernandez scooped one over the Poland goal 10 minutes from time, but it was Mbappe who scored France's third, with the attacker placing one into the top corner in the 91st minute after finding space inside the box.
The 23-year-old now has five goals at this year's competition and nine in the World Cup overall.
Poland were awarded a penalty in the final moments for a Upamecano handball; Lewandowski saw his initial effort kept out by Lloris, but the goalkeeper was off his line before contact was made, and the Barcelona striker found the back of the net from his second attempt.