However they well hung out to dry in the first period by Craig Shakespeare's side, going two up inside seven minutes with goals from Riyad Mahrez and Robert Huth before Jamie Vardy added another after Manuel Lanzini had pulled one back.
The Foxes showed no signs of a European hangover following their epic win over Sevilla, and although they may have a quarter-final meeting with Atletico Madrid on their minds Shakespeare knows they still need to get their domestic affairs in order.
Leicester captain Wes Morgan missed his first game of the season with a back injury which meant a rare appearance for Tunisian defender Yohan Benalouane in his place.
He has scored three goals in his last four Premier League games but Andre Ayew has not been able to win with West Ham since returning from the Africa Cup of Nations.
Schmeichel kept Leicester's lead intact in stoppage time with a reflex save to deny Carroll after Snodgrass's free-kick had been deflected into the striker's path.
The problems are piling up for West Ham manager Slaven Bilic, whose side have lost their last three matches and could yet find themselves in the relegation scrap.
West Ham: Randolph 6, Byram 5, Fonte 6, Reid 6, Cresswell 6, Kouyate 6, Obiang 6, Ayew 6, Lanzini 7, Antonio 6, Carroll 6. Within minutes of this decision, Leicester had again extended their lead when Vardy scored from close range, after a corner was not cleared by the Hammers inept defence.
NZ uninterested in hosting 2022 Com Games
Liverpool , in northwest England, has previously said it could be prepared to host the 2022 Games if they were not in Durban. Commonwealth Games Federation chief executive David Grevemberg offered his full backing to the organisers.
Subs (not used): King, Amartey, Zieler, Gray.
West Ham left the field at half time to boos from the home fans, who are now thoroughly fed up with the team's poor home form.
"You see centre-forwards go through that phase where they score and keepers, he has pulled off some crucial saves for us in the past couple of weeks".
"On the outside you try to keep and collected to keep the players focused".
"We made it a bit harder at the end and we were hanging on a bit". "I think hard work, commitment and endeavour, we showed all of them today, along with some good footballers".
"We said once the Champions League draw was made let's concentrate on the Premier League. We can recharge the batteries now".