Cole Palmer had a first-half penalty superbly saved by the Danish goalkeeper. It was the first Premier League penalty miss for the out-of-sorts Chelsea forward, who has now gone seven league games without a goal.
Ruud van Nistelrooy’s Leicester, deep in the relegation zone, looked dangerous on the counter, with Moroccan midfielder Bilal El Khannouss and Jamie Vardy linking effectively without finding the killer shot.
And they did not give up, substitute Ricardo Pereira drawing a save from Robert Sanchez in the 86th minute.
But they managed only three shots to Chelsea’s 20 and Sunday’s loss left them on 17 points, second bottom of the table and six points from safety.
Chelsea leapfrogged Manchester City, who lost to Nottingham Forest on Saturday, into fourth spot on 49 points, two behind third-placed Forest and 21 adrift of leaders Liverpool.
Before meeting second-placed Arsenal next weekend, the London side face Copenhagen in the Europa League at home on Thursday with a 2-1 lead from the first leg.
Europe-chasing Bournemouth were left kicking themselves as they squandered a two-goal lead to draw 2-2 at Tottenham Hotspur.
Andoni Iraola’s side were deservedly two goals up and set to boost their top-four hopes after Marcus Tavernier and Evanilson netted either side of halftime.
Pape Matar Sarr threw Tottenham a lifeline with a speculative cross that looped over Bournemouth goalkeeper Kepa. And soon after that Kepa brought down substitute Son Heung-min in the area with the South Korean converting the resulting penalty.
Bournemouth, for whom Justin Kluivert had a goal disallowed and hit the post, moved up a place to eighth spot with 44 points as Tottenham stayed 13th with 34.
_Reuters_