Lacazette almost had his second of the night just minutes later, but Leicester keeper Kasper Schmeichel turned the shot aside, but Giroud beat the Dane with an exquisite header on the ensuing corner to give Arsenal the 4-3 victory.
But Arsenal's defence, with essentially two full-backs playing in their back three, were soon caught out having been given a warning when want-away Leicester winger Riyad Mahrez volleyed wide. It's fantastic Giroud wants to stay - he chose to stay.
Giroud told French broadcaster SFR Sport: "We really have a good relationship with Alex, on and off the pitch".
"We kept going and the spirit of the team was absolutely outstanding", Wenger said.
He added: "I know how important Giroud is, not only as a player but in the group as well".
However, there was still one more goal to come in a pulsating first-half, with Danny Welbeck netting from close-range after good play from Kolasinac.
"Of course you can not afford to concede three goals at home".
The Gunners, who did lift the FA Cup last season, won the first trophy on offer to them last weekend when they beat Chelsea in the Community Shield on penalties at Wembley.
"They had two half-chances and put them in and we had to chase again and I thought going in at 2-2 at half-time it was our advantage, but then the corner gave them the advantage again and we had to chase again".
"It was a relief Giroud chose to stay". "Even when I played Giroud through the middle and him on the left he did very well on the left".
"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", Wenger told BBC.
Giroud, 30, started just 11 Premier League matches last season and scored 12 goals.
"I genuinely do believe in a season where we saw (Claudio) Ranieri sacked (at Leicester) after winning the league that we should reward and praise when club's show the ultimate loyalty and sticking with the manager". Both Lacazette and Giroud need strong seasons to make sure they are in the French party travelling to the World Cup in Russian Federation next summer.