The Reds' poor showing in front of goal has left them seven points behind Manchester United heading into the business end of the season.
The home side controlled much of the game and will be kicking themselves for not taking the lead in the first half after wasting a hatful of chances.
Bellamy's deflected goal early in the second half almost meant Mark Hughes' side took maximum points back to Eastlands, before Dirk Kuyt's effort 12 minutes from the end saved a point for the home side.
Liverpool manager Rafa Benitez made three changes from the side that narrowly beat Portsmouth 3-2 at Fratton Park two weeks ago with Lucas Leiva, Albert Riera and Kuyt coming into the starting 11.
There were no nerve-jangling changes by City manager Mark Hughes though with only Netherlands international Nigel de Jong coming into the side that drew 2-2 in Copenhagen on Thursday night. He replaced winger Shaun Wright-Phillips who was serving the first of his three-match ban.
Liverpool unsurprisingly started the better of the two sides and could have taken the lead as early as the eighth minute. A long ball by captain for the day Jamie Carragher found the on-rushing Yossi Benayoun, but his cushioned pass was blazed wide by star striker Fernando Torres.
With The Kop roaring the home side on, Liverpool pressed for the opener and they would have been celebrating had Benayoun's free-kick from the edge of the area not struck the top of the wall.
City were made to defend for much of the period as Torres, Riera and Kuyt all went close, but still Shay Given was not forced into any serious action.
Despite Liverpool's pressure the away side should have gone into half-time leading. Fortunately for the Reds, City midfielder Stephen Ireland's poor effort was comfortably parried by keeper Pepe Reina, before the Irishman struck the side-netting with the rebound.
Benitez was a frustrated figure in his technical area as he saw his side show plenty of promise, but fail to capitalise on it in front of goal.
Liverpool were made to pay, as Anfield old-boy Bellamy gave City the lead after only six minutes of the second half.
Good work down the left-hand side by Vincent Kompany led to Bellamy being released and the Welshman's effort took a wicked deflection off Alvaro Arbeloa and spun past the hapless Reina.
City had their tails up after that and it showed as de Jong tried to curl the ball past the Spanish keeper from fully 40 yards out.
Ireland thought he'd doubled the visitors' lead after 66 minutes when he turned in Micah Richards' pinpoint cross, only for the linesman to have his flag raised for offside.
The home faithful soon began showing their dismay at Liverpool's inept display in front of goal.
But their anger turned to relief with 12 minutes remaining as the flying Dutchman Kuyt came to his team's rescue.
Benayoun's cross from the left was misjudged by Torres but, luckily for him, his strike partner Kuyt was on hand to fire past Given.
The Irish keeper's reputation as one of the best in the Premier League was justified shortly afterwards when he pulled off two world-class saves to deny Benayoun and Kuyt and leave Liverpool's chances of winning their first title since 1990 in tatters.