The two sides came into the weekend occupying the last two Champions League spots, before wins for Chelsea and Liverpool on Saturday nudged West Ham down to sixth place.
But David Moyes’ men showed they are up for the challenge of qualifying for Europe’s top club competition for the first time, going 3-0 up and holding on during a late Leicester rally to climb back into fourth.
The Hammers took the lead as Arthur Masuaku’s cross went through to right-back Vladimir Coufal, who cut back for Lingard to sweep the ball inside Kasper Schmeichel’s near post from the edge of the box.
Jarrod Bowen then beat the offside trap to race on to Issa Diop’s long ball and square for Lingard to tap into an empty net for his eighth goal in nine Premier League games since arriving on loan from Manchester United.
The 28-year-old forward, whose recent form earned him an England recall, then played a part in West Ham’s third goal right after half-time as Bowen poked in from Tomas Soucek’s pass to round off a clinical team move.
Kelechi Iheanacho pulled a goal back to give the visitors hope, before grabbing his 11th goal in 11 games in stoppage time, but the Hammers ensured they did not surrender a 3-0 lead for the second straight home game and move within a point of third-placed Leicester.
Leicester’s preparations had been disrupted with James Maddison, Hamza Choudhury and Ayoze Perez left out for breaching Covid-19 protocols.
The Foxes were possibly affected by the absence of Maddison, Choudhury and Perez and were lacklustre for the first hour.
West Ham’s opener was the result of some patient build-up play, but then Leicester only had themselves to blame as they were made to pay for playing a high line for the second goal and being dispossessed in their own half for the third.
Ricardo Pereira caught Masuaku in possession to give Iheanacho the chance to fire in from the edge of the box and, shortly after six minutes of stoppage time was indicated, the Nigeria striker scored again following a low cross by substitute Marc Albrighton.
Leicester almost salvaged a point as Wesley Fofana headed wide at the death but it was another quiet afternoon for Jamie Vardy. After a blistering start to the season, he has now scored once in his past 18 games.
The Foxes are eager to avoid another late-season collapse and their next three home games are against West Brom, Crystal Palace and Newcastle, but they will need Vardy to help ease the burden on Iheanacho, 24, who is enjoying the longest run of Premier League starts in his career and is now Leicester’s joint-top scorer with Vardy.
Manager Brendan Rodgers told BBC Sport: “We mentioned about starting quickly and we did anything but. It was a tough one to watch.
“It’s always easy to play when you’re 3-0 down, I don’t take much from getting back into the game. We were too passive to win an important game.”