Youri Tielemans' stunning first-half strike set Brendan Rodgers' side on their way to a thoroughly deserved victory as they climbed out of the Premier League's bottom tier.
Tielemans controlled James Maddison's cut-back with his thigh and then sent a dipping effort into the top corner of Jordan Pickford's goal.
Harvey Barnes scored his fifth league goal of the season in the closing stages, hitting a powerful shot past Pickford.
The visitors dominated the first half but missed several chances to take the lead.
The excellent Maddison struck the outside of the woodwork with a curling, long-range shot as Rodgers' team continued to create openings in the second half.
Dominic Calvert-Lewin was forced to leave the field with an injury just after the hour mark.
Due to their superior goal difference, the win lifts the Foxes up to 13th place.
Maddison's performance will make it hard for him to get into the England World Cup squad.
The 25-year-old was at the heart of the Foxes' best attacking moves but the visitors' finishing proved their downfall early on, Pickford producing a one-handed save to deny Daka before Barnes missed the target.
Maddison had a goal, but it wasn't included in his performance. He rattled the woodwork with an ingenious effort midway through the second half after being denied in the first half.
The first goal of the season was a contender for goal of the season from Tielemans. Despite his uncertain future, Rodgers has said he will continue to work with the 25-year-old.
Barnes beat Pickford with a ferocious effort after collecting Maddison's lay off.
After giving up 22 goals in their first eight league games of the season,Leicester have not given up a goal in their last seven.
Before the game, Frank Lampard had told his players to find consistency week-in, week-out after they had collected four points from their past two games.
The boss will have been disappointed with his team's performance against the Foxes, who shot 15 shots in the first half.
The hosts struggled for service in the first half and were guilty of wasting possession.
Alex Iwobi, who flashed an early shot wide after Gueye had robbed Boubakary Soumare of the ball, released Dominic Calvert-Lewin in the opening minutes of the second half but theEverton forward shot straight at Danny Ward.
While Maddison was able to improve his World Cup prospects, Calvert-Lewin's hopes of being included in Southgate's squad seem to be hanging in the balance after the 25-year-old's second half injury.
He went down clutching his left thigh and was replaced by Neal.