The Gunners got off to the flawless start, with record-signing Alexandre Lacazette scoring after just 94 seconds, via his his first-ever shot in the Premier League.
Though Arsenal began the second half on the front foot, Leicester created the cleaner chances, Cech rushing out of his box to tackle Vardy and then tipping over a shot by Riyad Mahrez, and after 11 minutes they went in front again.
Despite a Danny Wellbeck leveller on the stroke of halftime, the Emirates Stadium crowd was growing increasingly anxious and, when Vardy scored his second with 40 minutes to play, they must have feared the worst.
Instead, Wenger avoided a third successive season-opening loss at the start of his new two-year contract.
Alexandre Lacazette's arrival has bumped Giroud even further down the Arsenal pecking order, but having given the 30-year-old the chance to leave, Wenger was thrilled he made a decision to stay.
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.
It took Lacazette just 94 seconds to score in the Premier League with his second touch in England's top-flight.
Former Arsenal legend Paul Merson believes Arsenal will get off to a winning start this season.
On his debut, Lacazette did some good work from out wide, showing he is a team player and creator too.
Honestly, you could not have asked for more to open the Premier League season for the 2017-18 campaign.
Jamie Vardy was there at the right time.
"You've got the season ahead to look forward to and everyone's raring to go".
Arsenal have also reportedly offered Sanchez a new contract worth £300,000-a-week as they look to shut down rumours linking him with a move to Manchester City.