The Paris Saint-German forward now has a tournament-leading five goals and the 2018 champions are within three wins of defending their title.
Robert Lewandowski scored from the penalty spot in second-half stoppage time for Poland.
No country has repeated as World Cup champions in six decades — since Brazil achieved the feat by claiming consecutive trophies in 1958 and 1962. Italy is the only other nation to have won two straight, in 1934 and 1938.
France’s quarterfinal opponent will be either England or Senegal.
Mbappé scored his first in the 74th minute when he was left unmarked to blast in a long-range shot following a counterattack. He added another in stoppage time when Poland goalkeeper Wojciech Szczęsny could only get a weak glove on another powerful shot from the man in the No. 10.
Having also provided two assists, Mbappé has easily been the most productive player in Qatar.
Mbappé celebrated his second goal by waving his arms for the crowd to cheer louder. Then he hoisted himself up onto the crossbar shortly after the final whistle in another celebratory gesture in front of France’s fans.
The French team took the lead when Mbappé threaded a pass to Giroud and the AC Milan striker quickly slotted the ball into the far corner. It was Giroud’s 52nd career international goal — breaking a tie with Thierry Henry on France’s all-time scoring list.
After Mbappé leaped into Giroud’s arms to celebrate, pumping his fists, Giroud held up seven fingers to the cameras — five on one hand and two on the other for “52.”
It’s all the more sweet for Giroud because he wasn’t even supposed to be a starter on this year’s squad until Ballon d’Or winner Karim Benzema was ruled out because of injury. Giroud also scored two goals in France’s opening 4-1 win over Australia.
France, however, wasn’t so sure to go this far when several other top players were ruled out shortly before the tournament because of physical issues, including midfielders Paul Pogba and N’Golo Kante, central defender Presnel Kimpembe, left back Lucas Hernandez, and forward Christopher Nkunku are also out.
On a record-setting night for France, goalkeeper Hugo Lloris matched the national team mark of 142 appearances held by Lilian Thuram.
The previous defending champion to reach the quarterfinals was Brazil in 2006 — when France beat the South Americans before eventually losing in the final to Italy in a penalty shootout.
With two European teams playing, there weren’t all that many supporters of either country inside Al Thumama Stadium except for small pockets of France fans beating drums behind one goal and red-and-white clad spectators chanting “Polska” behind the opposite goal. There were also plenty of empty seats.
Poland again struggled to get the ball to Lewandowski, a two-time FIFA player of the year.
While Lewandowski did miss wide on one long-range opportunity early on, he also gestured angrily at his teammates for not providing him with the ball.
Lewandwoski’s first penalty attempt in the final seconds was saved but he scored with the second after a video review ruled that Lloris left his line too early.