The Chelsea star went into the game on 40 goals, one behind the France and Juventus great. Now only Thierry Henry stands in front of Giroud, who scored twice in the first half against the eastern Europeans to leapfrog Platini in the standings.
Eduardo Camavinga got Didier Deschamps' charges off to a perfect start with a goal after just nine minutes, by way of a wonderfully executed overhead kick.
The stage was then set for Giroud to dominate, as he netted twice in the space of 10 minutes to put France well ahead of their opponents and bring his own international goal tally to 42.
France would go on to defeat Ukraine 7-1 on the evening as Deschamps' side dominated their opponents.
Giroud will now be gunning for Henry, who leads the way for his nation with 51 goals in 123 caps.
It was the perfect way for Giroud to celebrate a special landmark, as he made his 100th appearance for his country against Ukraine.
Just seven players have previously completed their century, with Lilian Thuram sitting at the top of that list as the most-capped Frenchman of all time with his 142 appearances.
Henry, Marcel Desailly, current No 1 Hugo Lloris, Zinedine Zidane, Patrick Vieira and Deschamps are the other players to have managed that feat.
2 - Eduardo Camavinga has become France’s 2nd youngest player ever to score for Les Bleus (17 years and 11 months), only behind Maurice Gastiger against Switzerland in March 1914 (17 years and 5 months). Wonder.#FRAUKR pic.twitter.com/JcEKtLf41o— OptaJean (@OptaJean) October 7, 2020
He did not disappoint, making further history as the second-youngest France international ever to hit the back of the net.
Maurice Gastinger holds both historic marks after breaking into the team in 1914 aged 17 years and 128 days, slightly younger than the midfielder who turns 18 next month.