The visitors, finding their groove after the international break, hogged the ball from the kick-off and Nicolas Jackson gave them a deserved early lead.
But they failed to make the most of their superiority until 15 minutes from time, when Enzo Fernandez scored to make it 2-0, before surviving a nervy few minutes after Jordan Ayew pulled a goal back for the home side.
Chelsea's win, which came after two draws, lifts them to 22 points -- one behind City and three clear of fourth-placed Arsenal ahead of the later kick-offs on Saturday.
It was Maresca's first game at the King Power since he took Leicester back to the Premier League last season in his only campaign at the club.
Chelsea zipped the ball around with confidence in the opening stages on a soggy afternoon in the English Midlands.
Joao Felix, making his first Premier League start of the season, fired wide in the 13th minute and then a minute later volleyed over from just outside the box.
But moments later Chelsea got the goal they deserved when Jackson won his tussle with Leicester defender Wout Faes, who missed a number of chances to clear.
The ball fell to Fernandez, who found Jackson and the Senegal forward poked home with the outside of his right foot for his seventh league goal of the season.
Leicester goalkeeper Mads Hermansen kept out Noni Madueke's sharp effort and Madueke had a goal disallowed for a tight offside against Marc Cucurella just after the half hour.
But as the first period wore on there was a momentum shift and Leicester suddenly started looking more dangerous.
Steve Cooper's men broke at pace and Oliver Skipp found Kasey McAteer on the right.
McAteer, making his full Premier League debut, cut inside but steered his shot just beyond the far post.
Wilfred Ndidi then screwed wide as half-time approached.
Chelsea looked certain to double their lead 10 minutes after the restart but somehow contrived to squander the chance, when Madueke got in the way of a Cole Palmer shot on the goalline.
It came after Hermansen saved Jackson's shot.
England international Madueke did his best to try and jump out of the way of Palmer's effort but it hit him and rolled out for a goalkick, with Palmer seeing the funny side.
But Chelsea did find the net in the 75th minute when Fernandez headed home after Hermansen kept out Jackson's header.
Leicester substitute Ayew pulled a goal back from the penalty spot deep into stoppage time after Bobby De Cordova-Reid was brought down but it was too little, too late.
Leicester, the 2016 Premier League champions, remain just three points above the relegation zone.
Cooper's problems mounted this week, with the Leicester boss announcing winger Abdul Fatawu would miss the rest of the season because of a "serious" knee injury.
