Chris Wood headed his ninth goal in as many matches since joining the Foxes from West Brom at the start of the year before Harry Kane marked his home debut with a goal.
Leicester dominated the first half with goalkeeper Kasper Schmeichel a mere bystander, aside from a stunning save to keep out a Morton Gamst Pedersen volley with the game goalless.
A comparatively quiet second half ended with Andy King heading a third in stoppage time.
After five straight league wins at the turn of the year, it ended a three-game run without a victory and moved the Foxes within five points of second-placed Watford with a game in hand on Gianfranco Zola's team.
Craig Dawson continued his fine start to life at the Reebok Stadium as Bolton dented the survival hopes of basement boys Peterborough with a 1-0 victory.
Dougie Freedman's side are unbeaten in five games since Dawson arrived on loan from West Brom in the January transfer window.
The central defender scored twice in Saturday's 4-1 thrashing of Hull and grabbed the only goal this time with a firm header from Jay Spearing's fifth-minute corner.
Bolton proved far superior to their opponents in the first half, but lost their way after the interval and were grateful for Peterborough's lack of penetration.
While Freedman will retain hope of a late play-off push, with his side now up to 10th, Posh remain at the foot of the table and face an uphill battle to avoid relegation.
Mark Robins claimed his first victory as Huddersfield boss as James Vaughan's second-half goal gave them a 1-0 victory and moved them six points clear of the relegation zone, further denting Burnley's slim promotion aspirations.
The Terriers, who took all the spoils at Turf Moor for the first time in 41 years, had scored just once in the previous four league fixtures but Vaughan produced a predatory finish with their first real chance of note 10 minutes after the interval.
In contrast, the Clarets were profligate with their finishing, Danny Ings, Charlie Austin and Sam Vokes all wasteful as they failed to find the net for a third successive outing and extended their winless streak to six games.