The AC Milan striker scored his 52nd goal for France to claim the country‘s all-time record, surpassing the great Thierry Henry.
The historic goal came just before half-time after Giroud controlled a pass from Kylian Mbappe before scoring low into the net just out of Wojciech Szczesny’s reach.
But having provided the assist for the opening goal, the brilliant Mbappe turned in style by scoring two terrific goals in the second half.
He hit a powerful shot into the roof of the net from 16 yards for his first and scored a wonderful second in stoppage time to take the lead in the Golden Boot race with five goals.
Didier Deschamps’s side had been frustrated until the first game and could well have been left behind.
Poland’s best start in the first half came when the ball fell to Piotr Zielinski in the center of the penalty area, but his shot went straight to Hugo Lloris.
Robert Lewandowski did achieve some consolation for the Poles, shooting a penalty with the last shot of the match.
Giroud’s 52 goals have come in 117 appearances, since his senior international debut at the age of 25 in 2011.
Followers of English Premier League football may have thought Giroud was past his prime when he left England after 10 seasons with Arsenal and Chelsea to join Milan.
But the 36-year-old scored 14 goals in all competitions last season and helped the Rossoneri to the Serie A title for the first time in 11 years.
In his 117th match, Giroud was desperate for that record goal against Poland, grimacing and shaking his head whenever an opportunity presented itself.
He had a great chance when Ousmane Dembele fired a cross cut on goal, but he couldn’t get enough contact with the ball and sent it wide.
He was presented with another great moment in the 44th minute, and this time he scored before being mobbed by all of his teammates during the celebrations.
France will see another of their national records broken if captain Lloris aligns in the quarterfinals to earn a 143rd international cap that sees him edge past legendary defender Lilian Thuram.
But it was Poland who had goalkeeper Szczesny to thank for just a goal down at half-time.
The Juventus goalkeeper dealt with a low shot from distance from Tchouameni, a shot from Dembélé after a choppy run and a shot from Jules Kounde from close range.
However, Szczesny could not stop Mbappé from breaking another record, as he surpassed Pelé’s tally of scoring seven World Cup goals before the age of 24.
The goals came from similar positions in the penalty area to take his World Cup goals to nine in 11 matches.
He has scored 16 goals in his last 14 games for France and 33 overall in 63 appearances.
Barcelona striker Lewandowski barely sniffed but scored further consolation in the 99th minute from the penalty spot, after Lloris went off his line too quickly to save the first try.
The Poles are now winless in their last eight meetings against France.