- Kevin De Bruyne (49')
De Bruyne's strike in the 49th minute curled around the wall and hit the inside of the left post before crossing the line, leaving no chance for Leicester goalkeeper Danny Ward.
With top goalscorer Erling Haaland missing a Premier League game for the first time since arriving at City through injury, the visitors lacked a cutting edge in the first half, with Leicester containing them with ease.
Leicester applied pressure in the late stages of the match, but could not find an equaliser despite an excellent long-range effort from Youri Tielemans which forced Ederson to make an oustanding save.
"We made it difficult for ourselves, we were a bit tired. They were very negative for 70 minutes but then their changes made it a different game. We didn't keep the ball in their half but we still could have scored a second," De Bruyne said.
"The free-kick goes perfectly, luckily it's 1-0. Ederson has been great, sometimes we only talk about his distribution but he's a great keeper and he proves it every week.
"We have proved we can win with or without Erling Haaland."
Leicester defended well throughout the match, with City manager Pep Guardiola praising their organisation.
"They changed it and it was a difficult game, because they had 10 players so deep and it's so difficult," Guardiola said.
"After we scored the goal they changed their rhythm and in the Premier League the last few minutes are always difficult. It's a massive victory for us.
"Kevin de Bruyne is back. He was not playing good the last few games but today he was amazing. He knows it. There was no space today, we had to be patient."
With the win, City maintain their unbeaten streak when they have scored first in the Premier League this season and move back into the top spot with Arsenal to play on Sunday.
Information from Reuters contributed to this report.
- Robert Jones
|Brighton & Hove Albion||13||6||4||3||+5||22|
|West Ham United||13||6||2||5||0||20|