With his first goal, Giroud surpassed Thierry Henry to become France's all-time leading scorer. The 36-year-old has benefited from Karim Benzema's absence from the competition.
The Paris Saint-Germain attacker then increased France's lead in the 74th minute before scoring again late on, giving Didier Deschamps' team another outstanding performance.
In the last moments, Robert Lewandowski scored from the penalty spot, although it was only a small consolation for Poland.
On December 10, the defending champions will face either Senegal or England in the competition's quarterfinals.
Raphael Varane leaped highest inside the penalty area to meet a corner in the fourth minute, giving France a chance, but the center-header back's went over the crossbar.
Mbappe's pace was causing all kinds of issues in a wide area in the early exchanges, and the crowd erupted everytime he touched the ball, making it difficult for Poland to exit their own half.
In the 13th minute, Wojciech Szczesny had to dive to block a hard shot from Aurelien Tchouameni before the Poland goalkeeper stopped Ousmane Dembele.
Szczesny next stopped Antoine Griezmann at close range before Lewandowski missed a shot down the other end of the field well short of Hugo Lloris's post.
When Dembele found space down the right before sending a low cross into the Poland box in the 29th minute, France had another fantastic opportunity, but Giroud somehow missed the post.
The White-Reds were creating issues at the other end, with Matty Cash missing the post, but Mbappe's side-netting attempt in the 35th minute posed the biggest threat.
Late in the first period, Poland had a great opportunity when Piotr Zielinski found space inside the box, but Lloris stopped his first shot and Dayot Upamecano stopped his second.
In the 44th minute of the game, France took the lead when Giroud received a feed from Mbappe and found the back of the net to become his nation's all-time leading scorer.
Giroud's goal separated the two teams before halftime, but Zielinski nearly responded before the break when his drive was blocked into the side netting.
In the 57th minute, Mbappe had a shot deflected just past of the Poland goal, and then Giroud had a magnificent goal disallowed due to Szczesny's injury after he collided with Varane and stayed down.
In the 72nd minute, Kamil Glik headed over the France crossbar, but Mbappe's thunderous attempt in the 75th minute ended Poland's chances of winning the game.
Ten minutes from time, Theo Hernandez floated a shot over the goal of Poland, but Mbappe scored France's third goal, slotting a shot into the top corner in the 91st minute after finding space inside the box.
The 23-year-old has scored five goals so far in this World Cup and nine overall.
In the dying seconds, a handball by Upamecano resulted in a penalty kick for Poland. Lewandowski saw his first attempt saved by Lloris, but the goalie was off his line before contact was made, and the Barcelona striker scored on his second try.