In the league's first Friday night start, Arsene Wenger's side was trailing 3-2 with seven minutes remaining but Ramsey grabbed the equaliser and Giroud headed in an 85th-minute victor.
Lacazette almost had his second of the night just minutes later, but Leicester keeper Kasper Schmeichel turned the shot aside, but Giroud beat the Dane with an exquisite header on the ensuing corner to give Arsenal the 4-3 victory.
Jamie Vardy made it 2-1 with an easy tap in the 29th minute but Danny Welbeck restored parity for the Gunners just before half time.
"Not only as a player, he is a fantastic player, but as well in the group".
Giroud had been seriously considering his future following the £52 million club record signing of Alexandre Lacazette and Wenger's certainty but has been persuaded to stay in what is now a "super sub" role.
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The player went on to enjoy three stellar campaigns with the Colombian club before he was signed by Ajax only last summer. He is an indispensable part of the club and that is proven by the fact that he appeared in all but two games last season.
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However, Wenger insists that Giroud will remain in north London beyond the end of the transfer window despite being given the opportunity to move on and seek more regular football elsewhere.
Having seen his Arsenal side win just one of their last seven opening fixtures, Wenger was staring at another defeat but was ultimately left satisfied with the victory.
"If you were a manager and you were on the bench, 3-2 down with 20 minutes to go and you win 4-3, you're more happy than concerned you know".
"I feel as well that the goals we conceded, we can work together to get rid of that because one was a corner, one was a ball we lost in the build up and the third goal was on a corner again, so we conceded two goals on corners".
"With the first corner, we were late".
It's only the second time in eight seasons that Arsene Wenger's side have secured three points in their opening fixture.