The Frenchman and fellow substitute Aaron Ramsay scored in the final seven minutes as Arsenal twice came from behind, the Welshman levelling two minutes before Giroud headed the decider.
Wenger revealed after Friday's win that Giroud, who has scored 97 goals in 231 appearances since joining from Montpellier in 2012, could have left the Gunners this summer.
Arsenal opened the scoring in the second minute but the Foxes hit back to lead 2-1 and then 3-2 before the Gunners' spectacular comeback in the closing minutes.
Record signing Alexander Lacazette opened his account within two minutes of the kick-off, but the home side's lead was nearly immediately rubbed out as Shinji Okazaki equalised minutes later before Jamie Vardy put the visitors in front after half an hour. It's interesting. Let's say the referee tends to let play continue. and you only really understand that when you experience it. I know how important he is not only as a player but also in the group he has a big weight.
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Giroud had been seriously considering his future following the £52 million club record signing of Alexandre Lacazette and Wenger's certainty but has been persuaded to stay in what is now a "super sub" role.
"Top quality game and you want PL to be best in the world and you have to produce games like that", Wenger told reporters.
Manager Arsene Wenger this week revealed that he gave the player the option of leaving, but that he chose to fight for his place. "He has a big weight in the squad and it was a relief for me that he chose to stay". That's how it came about but I think it was perhaps too early to celebrate because we didn't know how the match was going to pan out.
"It's simple, in every game he is stronger since he joined us", Wenger said. "We love him and in the end he chose to stay".
Leicester showed some of the form that won them the title in 2016 and helped stave off relegation last term but in the end they were undone by canny France worldwide Giroud who has been linked with a move away from Arsenal all summer.