The Citizens were dealt a major blow before kickoff as goal machine Erling Braut Haaland was not named in the matchday squad due to a minor foot injury.
However, a moment of magic from Kevin De Bruyne was enough to help the reigning Premier League champions edge past Leicester and move above Arsenal - who face Nottingham Forest on Sunday - to the top of the table.
Leicester, meanwhile, saw their three-game unbeaten run come to an end and they remain 17th in the table, for now, two points above the relegation zone.
Pep Guardiola made seven changes to the side that drew 0-0 with Borussia Dortmund in midweek, with Julian Alvarez handed a start up front in the absence of Haaland.
City unsurprisingly dominated proceedings in the first half, but they were frustrated by Leicester's robust back-five set-up and struggled to create many clear-cut chances.
After an uneventful first 45, the game came to life after the interval and the visitors made the breakthrough in the 49th minute courtesy of a stunning 30-yard free kick from De Bruyne.
After Jack Grealish was brought down by Nampalys Mendy on the edge of the penalty area, City's No.17 stepped up and curled a delightful effort over the wall, with his strike hitting the post on its way into the top corner.
De Bruyne's special set-piece strike is Man City's first Premier League goal from a free kick since Raheem Sterling curled one in at home against Crystal Palace in January 2021.
Leicester came close to restoring parity just a few minutes later when a ferocious 20-yard volley from Youri Tielemans was superbly tipped onto the crossbar by goalkeeper Ederson.
Substitutes Patson Daka and Kelechi Iheanacho both had half-chances for the Foxes in the final five minutes, and De Bruyne almost set up Ilkay Gundogan for a second in stoppage time, but the Citizens eventually held on to claim maximum points.
Man City failed to score in each of their last three away games across all competitions prior to their visit to the King Power Stadium, and even without the presence of Haaland, Guardiola's side found a way to record their ninth Premier League win of the season.
City will now turn their attention to Wednesday's Champions League clash at home against Sevilla before welcoming Fulham to the Etihad Stadium for their next Premier League fixture on November 5, while Leicester will prepare for next weekend's trip to Everton.