The hosts' joy was short-lived, however, as Shinji Okazaki equalized for the Foxes within minutes.
Giroud came big for the Gunners once again.
The match was a great advert for a league that is already prime box office viewing worldwide but Arsenal's hopes of a first title since 2004 will require some polishing of a rusty defence after Leicester put away half of their chances.
Arsenal record-signing Alexandre Lacazette launched his English league career in style by heading in the opener after 94 seconds.
Two minutes later, the comeback was complete, with super-sub Giroud sending the home fans wild via magnificent header from a Xhaka corner, despite being held by Wes Morgan.
But after deciding to stick it out for a sixth season at Arsenal, Giroud was the north London club's match-winner on the opening day of the new Premier League campaign after coming off the bench.
"At one stage I opened the door for him as I knew I had many strikers, and in the end he made a decision to stay", said Wenger.
"Not only as a player, he is a fantastic player, but as well in the group".
"I prefer to be on the pitch", the 30-year-old Giroud said, "but as much as I can I try to help the team reach its target".
"It is a relief and I believe as well a reminder to the players that they have hurdles on the way and that we can get round it, like tonight so that is quite positive".
Asked if there was any update on Sanchez's situation, Wenger replied: "No".
"I'm always looking for the positives, we came to the Emirates and the players executed the game plan".
"We saw it though for 83 minutes", Leicester manager Craig Shakespeare said, "and to concede two late set-plays in the manner we did is obviously hard to take".
"I think we have all seen the amusing business of the transfer window and we never know what is round the corner".
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.
"You win 4-3, you're more happy than concerned, you know", he added.
"The second goal was scored after a poor pass, which can happen, but we conceded the other two after corners".