In the 53rd minute, the 37-year-old, who joined the west coast club after leaving AC Milan at the end of the previous season, scored from close range to give his team the lead.
Erik Thommy of Kansas City tied the score to send the match into overtime, where goals from Mexican defender Omar Campos and Sierra Leonean forward Kei Kamara completed the victory.
Giroud, who became the record goal scorer in France with 57 goals when he retired from active duty in July, needed it following Columbus Crew’s defeat in the League Cup final in August.
Giroud remarked, “I came here to play that kind of final and to win trophies.”
I felt a great deal of sadness and disappointment for the team after the League Cup.
Even though these past few weeks have been challenging, we have remained united and genuinely wanted to win this title for the club and its supporters. It is important to me and the boys, and I’m thrilled to have contributed to the team and scored in this championship game.”
The win maintains LAFC’s chances of winning both the domestic league and the cup.
There are only three clubs that have completed the double; LA Galaxy did so in 2005, following in the footsteps of DC United and Chicago Fire.