But Arsene Wenger's double change turned the game, FA Cup final hero Ramsey drilling in an 83rd-minute equalizer and Giroud notching the victor two minutes later with a header that hit the bar and bounced over the line.
"The quality of their players, their fan base and the money that they can spend, they've always been unsafe", Leicester manager Craig Shakespeare said.
However, there was still one more goal to come in a pulsating first-half, with Danny Welbeck netting from close-range after good play from Kolasinac.
Danny Welbeck almost finished off an attacking move for Arsenal after a few one-touch exchanges with Mesut Ozil but his shot was blocked by Harry Maguire.
Arsenal also pursued Lacazette previous year before finally reaching a deal with Lyon this summer that could be worth up to £52 million.
Those subs forced a desperate defensive reshuffle which saw a winger (Oxlade-Chamberlain) at right back, two left backs (Nacho Monreal and Sead Kolasinac) at center back and a right back (Bellerin) at left back, and some of the reasons for this disjointed display were due to Laurent Koscielny, Shkodran Mustafi and Per Mertesacker all being unavailable.
The last player to score a goal faster on their Premier League debut was Thievy Bifouma, who came on for his Premier League debut for West Brom at half-time and scored after just 36 seconds in a 3-1 defeat at Crystal Palace in February 2014.
Arsenal got their campaign off to a winning start. Too early to start pointing fingers at our defence as we had only one natural CB play in defence but our attack was terrifying without our explosive star man Alexis Sanchez. So Jose Mourihno has strengthened in the areas he's needed to and they look stronger and will challenge for the title.
"Previously in the Premier League we've not got off to the best of starts, so it meant a lot for us to get a good start and get three points today".
"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". The first was a kick off.
And the 30-year-old proved his worth with another vital goal after coming on as a substitute - but is hoping for a more substantial role at the club. If Alexandre Lacazette can handle the workload, Arsenal should be fine against a lesser opponent. "As a game is in 90 that would guarantee you a goal".
It seemed like both teams were itching to get on the pitch to score goals.