Andre Ayew got West Ham's second just after the hour mark to usher in a tense ending, but Schmeichel proved too good as he pulled off several brilliant stops during the final stages.
West Ham United's Cheikhou Kouyate (left) and AFC Bournemouth's Charlie Daniels (right) battle for the ball during the Premier League match at the Vitality Stadium, Bournemouth.
Craig Shakespeare insisted he has no secret formula despite guiding Leicester to a fourth straight win. "The players think that's when they are at their best so that's what we'll encourage them to do".
Riyad Mahrez, Robert Huth and Jamie Vardy - three of the main protagonists of last season's title triumph - stunned the Hammers with first-half goals.
"It doesn't look good with Winston [Reid] and now it looks like Michail [Antonio] won't be able to go with the England squad", the Croatian said.
Ultimately, though, Shakespeare's side showed enough grit in the absence of injured captain Wes Morgan at the back to double their points won on the road this season.
West Ham haven't been in the game at all but now it's game on.
However, Vardy restored Leicester's two-goal lead before half-time when he pounced on the loose ball after West Ham failed to clear Albrighton's corner.
The Senegal worldwide should not necessarily be axed from the starting eleven completely, as he is still one of West Ham's strongest performers. We said once the Champions League draw was made let's concentrate on the Premier League.
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).
Ayew was then guilty of a bad miss as he blazed over when one-on-one with Schmeichel, before Cheikhou Kouyate's effort from six yards out amid a goalmouth scramble was kept out by a combination of Leicester defenders.
Leicester will head into the contest having won their last three matches since Shakespeare succeeded Claudio Ranieri as manager, including victories against Hull and Liverpool in the league.
Shakespeare's side enjoyed a memorable 2-0 victory over Sevilla in the Champions League last 16 on Tuesday as the English champions extended their impressive run in the competition.