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.
Record signing Alexander Lacazette opened his account within two minutes of the kick-off, but the home side's lead was nearly immediately rubbed out as Shinji Okazaki equalised minutes later before Jamie Vardy put the visitors in front after half an hour.
Jamie Vardy of Leicester City scores his side's third goal in their Premier League opener, which they ultimately lost 4-3, against Aresnal on Friday night in London.
After the match, the Foxes' boss faced questions about his use of substitutions, with Kelechi Iheanacho coming into the match just before Arsene Wenger's side leveled through Aaron Ramsey from a corner, but pointed to the defending of set-pieces as the real issue.
Giroud then sent the previously despondent Arsenal fans wild when he headed the 85th minute victor from a corner, Leicester keeper Kasper Schmeichel only managing to turn the ball onto the underside of the bar before it bounced over the line.
Arsenal's victor also came from a set-piece, with Olivier Giroud heading home.
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And speaking after the game, the 30-year-old confirmed his intention to stay and fight for his place at Emirates Stadium. "I know how important he is not only as a player but also in the group". In the end he made a decision to stay and it was one of the great days of the recent weeks for me.
He added: "We started really well and I thought we could stay in control".
"I'm always looking for the positives, we came to the Emirates and the players executed the game plan".
"There were hard moments when we were down and we managed to get out of that and it's great to see".
"We were punished on every single mistake by a Leicester team that was very efficient going forward". We encourage our midfield players to play balls in behind.