But Arsene Wenger's double change turned the game, FA Cup final hero Ramsey drilling in an 83rd-minute equaliser and Giroud notching the victor two minutes later with a header that hit the bar and bounced over the line.
"I opened the door for him at some stage as it's important for him to play but I don't want him to go", Wenger said at the post-match news conference.
"With Lacazette it is simple", Wenger said. "It's a long time since we had so much quality [in attack]".
The Ramsey-Giroud rescue act spared Arsenal from a fourth season-opening defeat in five campaigns and enabled Wenger to start the season with victory for only the second time in eight years.
Arsenal have made a "huge breakthrough" in contract negotiations with playmaker Mesut Ozil, according to a recent report.
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.
Paris open to video games at Olympics
IOC president Thomas Bach has said that eSports are contrary to "Olympic rules and values of sport". Video games and eSports may have a chance of being part of the 2024 Olympics .
Kasper Schmeichel came to Leicester's rescue in the 62nd minute as he produced a fine save to deny Hector Bellerin from close range.
Within three minutes Leicester were level. We can't wait to see where the league goes from here.
Granit Xhaka's sloppy pass was picked up by Albrighton and he forged down the left flank before bending a sublime cross into the danger area that Vardy converted.
"I think we have all seen the amusing business of the transfer window and we never know what is round the corner".
England striker Vardy put the visitors 2-1 ahead just before the half hour, darting into the box to rifle another fine Albrighton cross past Cech after the winger had pounced on a poor square ball from Arsenal midfielder Mezut Ozil.
Again a set-piece proved Arsenal's undoing as Mahrez's in-swinging corner from the right was nodded in by Vardy.
Aaron Ramsey equalised in the 83rd minute and two minutes later substitute Giroud rose highest to head home via the woodwork.
The late fight-back had the French manager lauding his team's "spirit" while he also praised their opponests for being clinical in the final third.