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.
England striker Jamie Vardy, who was heavily linked with Arsenal 12 months ago, scored a brace either side of a Danny Welbeck leveller that showed Arsenal's rearguard to be equally terrible from open play and set-piece situations.
"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 is really loved here, we love him and, in the end, he chose to stay".
Giroud's Arsenal future had been subject to considerable doubt after five years, with the £46.5m ($60.4m) club-record signing of Alexandre Lacazette expected to restrict his starting opportunities even further.
Wenger has always been desperate to keep Giroud because he offers something so different with his aerial presence but was also willing to let him leave if he felt that he needed a guarantee that he would start more regularly in this World Cup season.
"We had some avoidable goals which we conceded and overall we have to work on that", he said referring to poor marking in the by his team's defence. "We were quite good past year on corners and overall I believe that with a bit of work we can get that out of the system". I thought the ball would go out as it was flying over me and suddenly there was a player. He adapts slowly to the way we want to play.
Opening weekend activity continues later Saturday with Liverpool visiting Watford in the early match and six other contests starting later.