The new Premier League season began on a Friday, for the first time, with Arsenal hosting Leicester City.
But after Giroud's second-half introduction, his 85th-minute header proved decisive, grabbing Arsenal a vital three points.
Albrighton crossed for Jamie Vardy to put Leicester ahead after Xhaka had gifted the ball straight to him.
Although Danny Welbeck leveled on the stroke of halftime, Vardy restored Leicester's lead after the break.More news: Taylor Swift To Testify Against Former Denver DJ In Groping Case
Sanchez returned late to pre-season training with the Gunners due to his commitments at the Confederations Cup with Chile and will now have his start to the new Premier League campaign delayed.
Instead, Wenger avoided a third successive season-opening loss at the start of his new two-year contract.
The forward's header was too accurate for Leicester goalkeeper Kasper Schmeichel and landed right into the corner of the Foxes net.
Arsene Wenger has been the coach of Arsenal for about 21-years and just recently signed a 2-years contract extension at the beginning of the transfer window, after many had speculated his exit away from the club. Obviously, we'd love to see a continuation of what we saw against Chelsea, with perhaps a bit more finishing capabilities.
Vardy has now scored four goals in his last five premier league appearances against Arsenal.More news: Al Jazeera threatens legal action over Israeli censorship
"I have players coming back who have not played, like Mustafi. You want the Premier League to be the best league in the world and I think it has to produce this kind of games to produce interest and quality", he said.
Giroud, speaking after the game on the pitch with Sky Sports said: "Obviously I knew that I was going to have a chance so we tried to push".
Jamie Vardy then capitalised on very bad defending to twice put the Foxes ahead either side of Danny Welbeck's equaliser before Arsene Wenger sent on the cavalry.
Shinji Okazaki had Granit Xhaka in fairly close attendance, but was more determined thrusting himself at the ball to nod in from close range. "We kept going and the spirit of the team was absolutely outstanding", he said.More news: Taylor Swift uses photo in sexual assault Lawsuit