City were made to wait though until first-half stoppage time before taking the lead through David Silva and did not double their advantage until two minutes from time when substitute James Milner found himself in the right place.
Manuel Pellegrini’s team can count themselves more than a little fortunate to have claimed all three points given their lacklustre display, while the visitors also had two strong penalty appeals turned down either side of half-time.
But after a damaging loss to Liverpool last time out, a morale-boosting win at least ensures the gap to Chelsea stays at five points.
Had City’s £28m striker Wilfried Bony – making his first start for his new club on a night when skipper Vincent Kompany was dropped to the subs’ bench – had his shooting boots on in the opening 45 minutes then the game could have been over as a contest before the interval.
The muscular Ivorian first saw an early header cleared off the line by Esteban Cambiasso, before then being denied by a smart block at the near post by veteran goalkeeper Mark Schwarzer.
But Bony’s best opening came three minutes before half-time when, after being picked out by a delicious Silva through-ball over the Leicester back four, the forward blazed wastefully over the bar from six yards out.
In between those half-chances City winger Jesus Navas also tested the reflexes of the visitors’ 42-year-old shot-stopper, with Schwarzer doing brilliantly to divert the Spaniard’s 20-yards curler past the post.
Leicester, though, were not without their own moments of threat, particularly in a period midway through the opening 45 minutes when first Riyad Mahrez appeared to be bundled over in the box by Bony, but referee Robert Madley deemed it an accidental collision.
A minute later, club-record signing Andrej Kramaric was played clean through on goal by Mahrez’s fine pass, only for Hart to keep the scoreline goalless by dispossessing the Croatia international as he attempted to round the ‘keeper.
Nigel Pearson’s men were made to pay for that miss two minutes into injury-time at the end of the first period when Aleksandar Kolarov’s left-wing centre fell kindly at the feet of Silva, with the little Spaniard making no mistake from six yards out at the second time of asking.
But if that strike was meant to settle City nerves, it failed to do so, and it was Leicester who came closest to scoring next when Kramaric’s free-kick from the left-hand corner of the area was deflected inches past Hart’s near post.
The visitors were unlucky not to have been awarded a spot-kick in the build-up to the award of that set-play but the man in the middle adjudged Fernando’s foul on Kramaric to have taken place just outside the area when subsequent TV replays suggested otherwise.
When Mahrez hit the outside of Hart’s post with 17 minutes remaining, Leicester must have known their luck was out for the night and their resistance was finally killed off late on.
Navas, who impressed throughout down City’s right flank, put in a wicked centre which Milner, who had replaced Bony, tapped home to wrap up the points.
Manchester City: Hart (6); Sagna (6), Demichelis (6), Mangala (6), Kolarov (8); Yaya Toure (6), Fernando (6), Navas (7), Silva (7); Bony (6), Aguero (6)
Subs: Milner (7), Dzeko (6), Lampard (6)
Leicester City: Schwarzer (7); Simpson (6), Huth (7), Morgan (6), Upson (6), Konchesky (7); James (6), Schlupp (6), Cambiasso (6), Mahrez (7); Kramaric (7)
Subs: Vardy (6), Ulloa (6), Nugent (6)
Man of the match: Aleksandar Kolarov
Watch all of Wednesday’s goals on Sky Sports News HQ from midnight.