Shinji Okazaki scored a fifth minute equaliser, Jamie Vardy put Leicester ahead and Danny Welbeck levelled for Arsenal before halftime.
Arsenal's victor also came from a set-piece, with Olivier Giroud heading home.
Arsene Wenger has confirmed that Friday night's match-winner Olivier Giroud has made a decision to stay at Arsenal next season, ending interest from Everton, West Ham United and Marseille.
Leicester showed plenty of endeavour as they came close to causing an upset in the Premier League's first fixture.
ARSENAL'S ALEXANDRE LACAZETTE got his Premier League career off to the ideal start against Leicester at the Emirates this evening.
Two minutes later, the comeback was complete, with super-sub Giroud sending the home fans wild via magnificent header from a Xhaka corner, despite being held by Wes Morgan.
"At one stage I opened the door for him as I knew I had many strikers, and in the end he chose to stay", said Wenger.
Ronald Koeman's Everton have been most heavily mentioned in connection with the £25m-rated 30-year-old, with the likes of West Ham United, Marseille and Lyon also credited with an interest.
"It is fantastic", Wenger replied when asked about Giroud's willingness to fight for his place.
"To be honest, there was something in my soul and in my heart which told me to stay". Giroud is in his prime, at the top of his game.
"I think we have all seen the amusing business of the transfer window and we never know what is round the corner".
"You win 4-3, you're more happy than concerned, you know", he added.
"After that, let's take it game by game - go to Stoke - then to Liverpool, who are as well one of the teams who want to win the Premier League".
"I feel as well that the goals we conceded, we can work together to get rid of that because one was a ball we lost in the build-up and we conceded two goals on corners".
"It was good. Obviously I'm still getting used to the English game, the positives and negatives, shall we say, but I'm learning".
"The second goal was scored after a poor pass, which can happen, but we conceded the other two after corners".
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