Kewell Scores for Liverpool's Victory
Indeed, Liverpool's win pulled it level on points with second-place Manchester United, which won the Carling Cup, its first trophy in two years, with its 4-0 win over Wigan at Millennium Stadium in Cardiff, Wales.
Liverpool stays third in the Premier League but is eight points clear of fourth-place Tottenham.
Liverpool manager Rafa Benitez was frustrated with his team's lack of goals.
"I am not happy with the final scoreline. It was another 1-0 win and another really important three points, but I would like to see us score more goals," Benitez said.
"We certainly need to be able to finish games off when we do go ahead. At the moment when it is only one goal, you put yourselves under too much pressure."
Kewell scored in the 40th minute, racing on to a cross from Steven Gerrard to score inside the far post.
City went a man down in the 52nd minute when Joey Barton was sent off for a second yellow card.