Nacho Monreal's 87th-minute shot cannoned off Robert Huth into the net, handing Arsene Wenger's Gunners a win that looked beyond them at times.
Of more importance to Wenger than the performance will be collecting what could prove to be three invaluable points as fellow top-four hopefuls Manchester City and Manchester United face off on Thursday night.
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Arsenal XI: Cech; Gabriel, Koscielny, Monreal; Bellerin, Coquelin, Xhaka, Gibbs; Ozil, Alexis; Walcott
Subs: Martinez, Ramsey, Elneny, Oxlade-Chamberlain, Iwobi, Welbeck, Giroud
Leicester XI: Schmeichel; Simpson, Benalouane, Huth, Fuchs; Mahrez, Ndidi, Drinkwater, Albrighton; Ulloa, Vardy
Subs: Zieler, Chilwell, Musa, King, Amartey, Okazaki, Gray
WHAT THEY SAID
Arsene Wenger: "We have to fight like mad to win our games. The door is open [to the top four] but it demands a consistency from us.
"It is still possible, but we need a near perfect run-in. We need to keep the level of desire and hunger for every game of the season."
Craig Shakespeare: "Seeing ]Arsenal beat Man City], it didn't look like turmoil to me, there were players fighting and they thoroughly deserved the win in the end, even though it was a close game."