Leicester defender Jannik Vestergaard missed a golden chance from an early corner, but he could not get a clean connection on his header and it sailed over the bar.
City striker Ferran Torres had a number of decent chances in the first half but Kasper Schmeichel managed to avert the danger.
Harvey Barnes came close to opening the scoring early in the second half as he rose to meet a cross, only to send his close-range header skimming off the top of the crossbar.
A minute later, Jamie Vardy had a goal ruled out for offside but it was Manchester City who finally broke the deadlock as Silva pounced on a loose ball in the box to fire home in the 62nd minute.
City defender Kyle Walker almost added a second with a powerful shot from the edge of the box, but Kasper Schmeichel managed to get a hand to it and put it behind for a corner.
Leicester piled forward looking for an equaliser and Kelechi Iheanacho and Ademola Lookman both went close, but Ederson was alert and quick off his line to save.
With his pace and assured first touch, Vardy threatened throughout and City were delighted that they managed to withstand the wave of counter-attacks that often put them on the back foot in the last half hour.
"We did really well, the process we found and we let them run a lot. We know how dangerous Jamie Vardy and also Harvey Barnes are in transition. The players were able to be focused and to concentrate," City boss Pep Guardiola told the BBC.
"Kasper Schmeichel is a really top keeper so it sometimes happens. The good thing is the amount of chances we create. This is a good thing. Of course, we would have loved to score more goals," he added.
Manchester City moved up to second spot on nine points after four games, ahead of Brighton & Hove Albion and Tottenham Hotspur on goal difference and one point behind Manchester United. Leicester are ninth on six points.
"I thought we deserved something from the game. You have to stay in the game against a team of that quality but I thought we were excellent and created a lot of chances," Leicester manager Brendan Rogers said. (Reuters)

Real Madrid denies plans to appoint sporting director
UBA Pensions ready for annual sports meet
Forget Wilder, fight me; Fury tells Joshua
Onuachu lacks rhythm in Eagles setup – Lawal
Ukah faces Osigwe in historic all-Nigerian PFL clash
UCL: Lookman set for Atletico return against Barca
Organisers brace for National Schools Football tourney
Semi Final Teams Emerge As Coast Clear For Final Ceremony Of 7th U-13 JOF Kids Cup Tournament
Okoye keeps seventh clean sheet in Como draw
Nnadozie relishes FA Cup progress
Akpokona recovering well, doesn’t need assistance – Son
NOC Plans To Mark 2026 Olympic Day On June 27
Rangers International going, going . . . (63,689 views)
Amaju Pinnick: A cat with nine lives (55,010 views)
Second Term: Amaju Pinnick, Other NFF Heavyweights Home to Roost •How Pinnick Broke the Jinx (52,928 views)
Current issues in Nigerian sports: Matters arising (52,531 views)
Sports Development: Zenith Bank on the zenith (52,460 views)
Missing $150,000 IAAF Grant: Solomon Dalung’s Hide and Seek game (52,364 views)
Gov. Abdullahi Ganduje’s solid footprints, commitment to sports development in Kano State (52,223 views)
NFF Presidency: Pinnick, Maigari, Ogunjobi, Okoye in Battle for Supremacy (51,768 views)
Olopade, BET9A wave of revolution in NNL (50,955 views)
Commonwealth Games 2018: Shame of Muhammadu Buhari, Solomon Dalung (49,464 views)
Ibrahimovic’s Man U exit: Whose decision is it? And in whose interest? (47,870 views)
John Mikel Obi: Segun Odegbami’s Outrageous Call! (47,340 views)