Lingard scored twice in the first half to set the Hammers on course for a crucial victory over fellow Champions League hopefuls Leicester.
Kelechi Iheanacho pulled a goal back to give Leicester hope, before grabbing his 11th goal in 11 games in stoppage time, but the Hammers held on to ensure they did not surrender a 3-0 lead for the second straight home game and move within a point of third-placed Leicester.
Afterwards, Lingard stated: "We almost made a mess of it at the end. It has been like that for three games. We are still learning. We take the positives and negatives from the game. We always start really good and on the front foot. I am picking up good positions, where the ball is falling. It's confidence, instinct, knowing players and where the right and left back and going to put it.
"It is great. We are in something to fight for. Games are like cup finals. We grind out the wins and take the points home. The lads battle on. There is a big belief in the team. We take each game as it comes, step by step for top four. It would be a brilliant achievement. First time in West Ham's history in the Champions League."