Giroud came off the bench with Arsenal trailing 3-2 in Friday's Premier League curtain-raiser at the Emirates Stadium and after fellow substitute Aaron Ramsey equalised, he headed in an 85th-minute victor.
It didn't take long for things to get started, with Alexandre Lacazette giving Arsenal the lead in just the second minute of his debut as the most expensive signing in the history of the club.
Ibrahimovic's made the move from Ligue 1 to the English top flight last season, and managed to score 17 goals in 28 league appearances for the Red Devils, a return Wenger feels his new striker should try and match. It was one of the days of recent weeks for me because I know how important he is, not only as a player, he is a fantastic player, but as well in the group.
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.
Giroud appears willing - if a little reluctantly - to accept his role as an understudy to Lacazette.
"Lacazette is simple - in every game he's stronger".
The visitors took the lead again 10 minutes into the second stanza as Vardy grabbed his brace with a cute header from close range.
Last season was by far the most hard of Wenger's 21-year tenure as manager, with Arsenal's on-pitch travails exposing him to furious protests from sections of the club's support.
"I love the man and the player because he's a fantastic guy. committed (and) he loves the club", Wenger said. We had a lot of experienced defenders out injured for the game. "Because one was a corner, one was a goal where we lost the ball in the build-up and the third goal was a corner again". We have many games and hopefully I can give games to all the strikers. Leicester will be happy enough to see that they appear to have the goals in them this season, they just need to tighten up their back line against set pieces. But Leicester, which so astonishingly won the league in 2016, couldn't hold on for its first win at Arsenal since 1973.