David Silva broke the visitors' resistance in first-half stoppage time before James Milner came off the bench to wrap up the points late on and ensure the champions bounced back from Sunday's defeat at Liverpool.
Manuel Pellegrini's men started the evening five points behind leaders Chelsea having played a game more, and that is how they finished it despite being frustrated by Nigel Pearson's men for long periods.
Riyad Mahrez hit the post late on, while the hosts spurned a string of late chances before Milner's effort secured the spoils while Leicester remain rooted to the foot of the table, seven points from safety.
Home captain Vincent Kompany was surprisingly dropped as Pellegrini's response to Sunday's damaging defeat was to make five changes to his starting line-up, with Wilfried Bony also making his first start since his January move from Swansea.
The champions started in positive fashion too. Bony's full debut almost got off to the perfect start as he headed goalwards from Silva's third-minute corner, but Esteban Cambiasso was there to hack off the line.
Bony's chance appeared to set the tone for what was to come, but Leicester succeeded in frustrating their hosts, and grew into the game despite seeing little of the ball in the opening 20 minutes.
Jeffrey Schlupp then could have had a 23rd-minute penalty when clumsily felled by Bony, and Joe Hart had to rush off his line to stop Andrej Kramaric and spare Eliaquim Mangala's blushes two minutes later.
The hosts exploited the space created by a rare Leicester attack to get in behind and after two last-ditch blocks a yard from goal by Robert Huth and Wes Morgan, the ball fell into the Spaniard's path, allowing him to tap into the net.
But substitute Milner put the result beyond doubt when he darted across Morgan to convert Navas' perfect cross from the right with a low finish in the 88th minute.
