Gareth Barry put the hosts ahead in the 14th minute, Carlos Tevez claimed he had got the faintest of touches on Micah Richards' header seven minutes after the interval and the Argentinian converted a penalty.
Considering Liverpool regard City as their main rivals for a place in the top four the result could prove to be hugely significant - even this early in the season.
However, City boss Roberto Mancini was wary of reading too much into the outcome.
"I thought we played well. We need time to gel and improve because we were missing four or five important players," he said.
"But the team played with a good mentality. If they play with a good mentality I think we can beat every team.
"We beat a strong team like Liverpool, who can fight for the title.
"This win helped us believe in ourselves and this is important."
The match was Sheikh Mansour's first visit to Eastlands, having taken over almost two years ago, and Mancini was congratulated by him after the game.