Lingard, who has been in scintillating form since arriving on loan from Manchester United in mid-season, took his tally for the Hammers to eight goals with two strikes before half-time.
But what happened after that suggests West Ham fans will need to strap themselves in for the remaining seven games of the season as once again they turned a position of comfort into a one requiring extra sets of fingernails.
Leicester, weakened by the absence of Ayoze Perez, James Maddison and Hamza Choudhury who were omitted for a breach of COVID-19 protocols, finally began to show the intensity required and got a lifeline when Kelechi Iheanacho fired home with 20 minutes left.
West Ham, who squandered a 3-0 lead to draw with Arsenal last month and almost did the same against Wolves in midweek, looked nervy and Iheanacho ramped up the tension with a second goal in stoppage time.
Manager David Moyes paced the touchline frantically but West Ham survived six added minutes to maintain their quest for an unlikely top-four spot. They moved back above Liverpool and Chelsea with 55 points from 31 games, one point behind Leicester who suffered a second successive league defeat.
"We almost made a mess of it at the end. It has been like that for three games," Lingard said after the game. "We are still learning.
"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."
After Liverpool's last-gasp win over Aston Villa on Saturday and Chelsea's victory over Crystal Palace the pressure was on West Ham to respond against an injury-weakened Leicester side whose stranglehold on a top-four place is loosening.
While Leicester enjoyed plenty of early possession West Ham showed the clinical edge Moyes has instilled in them.
They took the lead in the 29th minute when Vladimir Coufal played the ball in towards Lingard who improvised a sensational first-time curling volley with his right instep which completely bamboozled Leicester keeper Kasper Schmeichel.
Leicester conceded again just before half-time when Bowen galloped down the right and crossed for Lingard who slotted into an empty net for his eighth goal in nine league games.
Lingard was also involved in the move which saw Tomas Soucek's pass set up Bowen to make it 3-0.
In a frantic finale, Schmeichel went forward at a Leicester corner and Wesley Fofana headed a great chance wide.