New signing Alexandre Lacazette gave Arsenal the lead with a debut goal just two minutes in just before Shinji Okazaki drew level just moments later.
Ramsey erased the one-goal deficit for the Gunners with a strike in the 82nd minute.
The fightback did happen however with Ramsey (83rd minute) and Giroud (85th minute) securing a 4-3 opening night win for the Gunners.
The Emirates was absolutely hopping at this stage and there was only ever going to be one outcome, the often maligned, Olivier Giroud, like Ramsey before him, came off the bench and scored the victor to send the stadium into raptures.
"He wanted to stay and that was one of the greatest days I've had in recent months".
And the 30-year-old proved his worth with another vital goal after coming on as a substitute - but is hoping for a more substantial role at the club.
Two goals in the first 10 minutes and two in the last 10 - if that doesn't rekindle the excitement of Premier League football, not much can.
"I'm convinced the team is focused".
Leicester showed some of the form that won them the title in 2016 and helped stave off relegation last term but in the end they were undone by canny France worldwide Giroud who has been linked with a move away from Arsenal all summer.
Leicester City was a hard opponent, but outmatched by Arsenal.
The Premier League made a thrilling return, and Arsenal finally had something to celebrate on the opening weekend.
Guardiola anticipates that he'll see an improvement in his defence but insists they need to be better at the other end of the pitch too if they are to compete for the Premier League. His first? The kick-off...
Oxlade-Chamberlain has always been regarded as one of the long line of Arsenal players, who are to be the future stars. Leicester exploited sloppiness by the Gunners to go ahead, leading to murmurings of discontent among the home crowd.