Fabio Borini had the first real chance of the match, but diverted Raheem Sterling's fine cross just wide of the post.
A minute later City hit the post through Carlos Tevez, who somehow dinked towards goal from the tightest of angles but the ball eventually came back off the post.
Liverpool started to control the game and after Vincent Kompany almost turned a Steven Gerrard cross into his own net. Martin Skrtel thumped in a bullet header from the resulting corner to give the hosts the lead.
It was a deserved lead for the Anfield outfit, and City were unable to create much else as the teams went in at 1-0.