But West Ham responded once more as they pulled another one back just after the hour mark - Andre Ayew nodding in from close range as the home side looked to ensure a tense ending for Leicester.
Ahead of this weekend's fixtures, Slaven Bilic's side are 11th in the table, some 14 points off the top seven, which was seen as a base target at the start of the campaign.
England would then have five teams in the Champions League next season, with United going into the play-off round and Leicester qualifying for the group stages. I would take anyone, there is not a bad team in there.
On frustration from joint-chairman David Sullivan after losing 3-2 at Bournemouth: "It was a comment on that game, and I said also we can't be happy with the way we performed and how we conceded the three goals".
"We want to train as normal and the preparation has to be for the West Ham game". The out-of-form strikers such as Jamie Vardy and Riyad Mahrez have regained springs in their step as they find traces of form in domestic circuit.
West Ham have lost as many games against Leicester in their last five (4), as they did in the previous 25 combined (all comps). If other teams come here they will obviously have to be wary of that.
"They'll probably defend well like they did against Sevilla and try to hit them on the counter attack and it will cause West Ham problems".
Kyrgios to face Federer in Indian Wells
Should Kyrgios defeat Federer as well, it could give us some big answers, thinks former doubles number one Todd Woodbridge. The rivalry between 14-time Grand Slam and the 18-time winners is one of the most exciting in the history of tennis.
Goals from club captain Wes Morgan and Marc Albrighton saw Leicester to a 2-0 win at the King Power Stadium on Tuesday, with Schmeichel making a key penalty save on the night as they sealed a 3-2 aggregate win over Sevilla following a 2-1 first-leg loss in Spain.
West Ham are Sky Bet's 5/4 favourites for the victory with Leicester up against odds of 21/10 to extend their winning run, while the draw is a 12/5 chance.
Leicester are two goals away from netting their 500th Premier League goal (498 currently).
It was a thrilling finale with West Ham looking most likely to score the next goal and they nearly did in stoppage time but for an outstanding save from Schmeichel, who somehow denied a Carroll shot from only a few yards out.
Since his debut in September 2012, Andy Carroll has appeared in just 94 of West Ham's 178 Premier League matches (53%) and played just 40% of possible minutes (6472).
And in stoppage time Schmeichel made a stunning point-blank save to deny Carroll as Leicester held out to take another big step away from relegation trouble, and continue to prove there is life in the champions yet.
Leicester have won all three of their matches under Shakespeare by a two-goal margin but are winless in their last 15 Premier League games on the road, failing to even score in the last four.