But Arsenal's pressure in the final half hour turned the game back their way and Aaron Ramsey equalised with seven minutes remaining before Giroud headed the 85th minute victor.
Shinji Okazaki scored a fifth minute equaliser, Jamie Vardy put Leicester ahead and Danny Welbeck levelled for Arsenal before halftime.
Pushed on whether he thought Giroud could leave before the transfer window closes on August 31, Wenger was adamant.
"You know, I must say I opened the door for him at some stage because I know that it's important for him to play". "He made a decision to stay and it was one of the great days of recent weeks for me".
It was only the second opening day victory in seven seasons for the Gunners who are coming off a torturous campaign that saw them finish outside the Champions League places for the first time in 21 years.
Juveniles copan lista preliminar de Uruguay para enfrentar a Argentina y Paraguay
Uruguay , 17° en el ranking FIFA recibirá a la Argentina , y una semana más tarde (el 5 de septiembre), visitará a Paraguay .
"If you were a manager, you're on the bench when you're 3-2 down with 20 minutes to go, and you win 4-3, you're more happy than concerned", said Wenger.
"Scoring three goals away from home is a positive and we'll get back on the training field to make sure we sort the problems out". "We were quite good previous year on corners and overall I believe that with a bit of work we can get that out of the system", the French coach added.
Leicester boss Craig Shakespeare was also pleased - even if the Foxes headed back to the East Midlands with nothing to show for their evening's endeavour. He adapts slowly to the way we want to play.
Shakespeare was true to his word and started Riyad Mahrez despite the Algeria worldwide asking to leave the King Power Stadium.
When asked if he expected Mahrez to stay, he said: "Who knows?" Riyad has been very focused.
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