Shinji Okazaki scored a fifth minute equaliser, Jamie Vardy put Leicester ahead and Danny Welbeck levelled for Arsenal before halftime.
The impressive Vardy scored his second in the 53rd minute to put Leicester in front once more, curling Riyad Mahrez's corner into the bottom far corner amid poor Arsenal marking.
"But I don't want him to go and in the end he chose to stay and it was one of the days of recent weeks for me because I know how important he is". It was one of the great days of recent weeks for me because I know how important he is.
Ever since France striker Alexandre Lacazette joined in July for a club-record 60 million euros ($68 million), the future of compatriot Giroud has been in doubt.
Arsene Wenger's side were seven minutes away from a miserable start to the new campaign after falling 3-2 behind at the Emirates Stadium. "I love the man and the player", said Wenger.More news: Two survive plane crash unreported for hours
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Asked if Giroud could still leave before the transfer window closes on August 31 until January, Wenger replied: "No".
"It's impossible to keep them happy when strikers don't play".
"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.
"I'm always looking for the positives, we came to the Emirates and the players executed the game plan".
Scroll through the gallery above to see how we think each Premier League team will get on during the opening weekend of the season.
'We wanted someone who would play attacking, attractive football, that is a core part of this football club, and finally someone who would give young players a chance.