The Gunners trailed 3-2 with seven minutes to go before Aaron Ramsey and Giroud swung the game back in the home side’s favour at a euphoric Emirates Stadium.
Alexandre Lacazette headed the Gunners ahead 94 seconds into his top-flight debut, only for Shinji Okazaki to nod in an equaliser just two minutes later.
Vardy then slid the visitors ahead from Marc Albrighton’s cross, before Danny Welbeck drew Arsenal level at the end of a pulsating opening half.
Leicester took the lead again when Vardy headed in Riyad Mahrez’s corner before Arsene Wenger made an inspired double substitution which sparked Arsenal’s comeback.
Substitute Ramsey smashed in an angled drive – from a corner which was won after Mesut Ozil handled in the build-up – before Giroud showed athleticism and strength to meet Granit Xhaka’s corner.
Giroud proves his worth after deciding to stay
Giroud’s days at Arsenal appeared to be numbered following the arrival of fellow France striker Lacazette from Lyon for a club-record £46.5m fee.
And Wenger revealed after Friday’s win that Giroud, who has scored 97 goals in 231 appearances since joining from Montpellier in 2012, could have left the Gunners this summer.
“At one stage I opened the door for him as I knew I had many strikers, and in the end he decided to stay,” said Wenger.
“He doesn’t want to leave and I’m happy he wants to stay.”
The 30-year-old wasted no time in proving his worth with another vital goal after coming on as a substitute.
Giroud offers a different, more physical option for Wenger, but is hoping for a more substantial role at the club.
Since the start of last season, he has scored seven Premier League goals when coming off the bench – three more than any other player in the same period.
“I prefer to be on the pitch as much as I can but I want to help the team reach the targets,” he said.
Arsenal rally to avoid another opening defeat
Arsenal started the new Premier League season having won just one of their previous five opening matches – all of which were also home fixtures.
In the build-up to Friday’s game Wenger repeatedly stressed the importance of beginning with a positive result against Leicester – and the Gunners appeared to have listened to their manager as they made the dream start.
Lacazette was perfectly placed to take advantage of Wes Morgan misjudging Mohamed Elneny’s cross, flicking in a low header to become the fastest-scoring debutant in Premier League history.
The joy did not last long, however. Leicester exploited sloppiness by the Gunners to go ahead, leading to murmurings of discontent among the home crowd.
Arsenal’s failure to finish in the top four of the Premier League for the first time in 20 years last season, not to mention the criticism Wenger has received from some sections of the Gunners support, meant the Frenchman could ill-afford to begin with a defeat.
And the mood ebbed and flowed inside the Emirates – with some of the familiar grumblings of discontent evident.
The atmosphere turned dark among the home fans after Vardy’s first, the audible frustration subsiding when Welbeck calmly rolled in Saed Kolasinac’s cut-back, only to return again when Vardy restored the Foxes lead.
Wenger looked on anxiously from the dugout, eventually appearing on the touchline when he introduced Ramsey and Giroud after 67 minutes.
Within 20 minutes both players had scored – and the mood completely changed – as Arsenal avoided losing their opening fixture for the fourth time in five years.
Leicester show glimpses of their title-winning form
Leicester manager Craig Shakespeare talked in his pre-match interview about the Foxes knowing their counter-attacking strengths and trying to use them to good effect against Arsenal’s “fashionable” back three.
That is exactly what they did.
The visitors found joy down the flanks, exposing the Gunners’ familiar defensive failings through Vardy’s sharp movement and quick balls forward.
Their rapid breaks were reminiscent of their title-winning side of two seasons ago, as was their clinical finishing: the Foxes scored with each of their three efforts on target.
Unfortunately for the 2015-16 champions, it was their own lapses of concentration which could not keep Arsenal out at the other end.
Led by captain Wes Morgan and new signing Harry Maguire, Leicester remained resolute in the second half until the pressure from Arsenal – who had 27 attempts at goal – eventually told.
“Scoring three goals away from home is a positive and we’ll get back on the training field to make sure we sort the problems out,” said Vardy, who turned down a move to the Gunners last summer.