Former Manchester United man Danny Welbeck also found the back of the net at the end of the first half, while substitute Aaron Ramsey scored the third goal just minutes before Giroud's victor.
Vardy's second goal, a towering header from a corner-kick, looked to have won it for the Foxes until the sensational finale that saw the game swing in Arsenal's favour.
But the thing with Chelsea is that they play to the system, are well drilled and the new signings will fit into that system which has shown works so well over the past 12-months.
Arsenal's new signing Frenchman Alexandre Lacazette took 94 seconds to make his mark with a header from Mohamed Elneny's curling cross to equal the record for the fastest opening goal in a Premier League season.
Pochettino forgives Rose for Spurs 'Google' jibe
We are so calm. "Over the last five years Tottenham have always signed players and spent money at the end of the window", he said. My words were not meant to offend and for that I would like to apologise to the chairman, manager, my team mates and the fans.
It was an incredible escape act from Arsenal, but Giroud claimed his team, who dominated possession and peppered the Leicester goal, never doubted they would hit back. We had a lot of experienced defenders out injured for the game.
After enduring a troubled campaign marred by fan protests against him last season, Wenger desperately needs a strong start this term. "He made a decision to stay and it was one of the great days of recent weeks for me". Not only as a player, he's a fantastic player but as well in the group.
Giroud had been linked with an exit during the summer, and Wenger admitted he considered allowing his most authentic target man to leave but the 30-year-old resisted the idea. At some stage, I opened the door for him because I knew that I had many strikers.
"We wanted to do that today - unfortunately that didn't happen and it's something where we can look back and analyse the game and see where we went wrong and improve on the situation".
Sharad Yadav is free to express his opinion, says Bihar CM
Yadav, who is on a tour of Bihar , has said he still believes he is a part of the grand alliance with the RJD and the Congress. This was their first in-person interaction since Nitish reconfigured his government in Bihar to include the BJP last month.
Seoul: Response will be strong if N. Korea acts
Speaking to journalists at his New Jersey golf club, the President said that he didn't think his comments had been "tough enough". Mattis praised the efforts of United Nations Ambassador Nikki Haley that resulted in a U.N.
West Ham United should look at Nikola Kalinic
First five games: Manchester United (A), Southampton (A), Newcastle United (A), Huddersfield Town (H), West Brom (A). The Argentine global has started to add more end product to his game and, at 24, his best days look in front of him.
Solar Eclipse Question? There's An App for That
In ancient India, he said, people believed that the severed head of a deity named Rahu caused eclipses by swallowing the sun. If you haven't placed an order yet - or your glasses are arriving after the solar eclipse - don't panic yet.