Chelsea were dominant with the Foxes suffering another slow start and Schmeichel got down to smother Willian’s low effort after 15 minutes.
The hosts were searching for their first double against Chelsea since 2000-01 but there was little urgency from Leicester, even with a top half place at stake.
Ben Chilwell, James Maddison and Tielemans launched efforts for Leicester but the game struggled to shake its end-of-season feeling.
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Scoreflashes from Brighton got the biggest reactions of the first half with eyes cast on the title race.
Vardy glanced a header from Chilwell’s free-kick straight at Willy Caballero after 31 minutes before both sides blew excellent chances to open the scoring late in the half.
First, David Luiz’s slip let Vardy through clear on the left but he opted to pass to Tielemans instead of shooting and his lay-off was woeful and the midfielder could only cut back to Caballero.