The Blues began the brighter of the two sides and made their domination count after 11 minutes. Juan Mata played in Brazilian midfielder Ramires, who beat Jose Enrique for pace before going on to place the ball inside Pepe Reina's near post.
Kenny Dalglish's Liverpool began to take control as the half drew to a close without calling Cech into any meaningful action.
The goal that would prove to be the winner for Chelsea arrived in the 52nd minute. Frank Lampard slotted a pass through to Didier Drogba, who shot across Reina's goal and into bottom right hand corner of the net.
Andy Carroll was introduced into the action as a response to Chelsea's second goal and the £35m striker made an almost instant impact in the 64th minute. Jose Bosingwa's attempted clearance ricocheted to Carroll, who turned John Terry before lashing the ball into the roof of the net from close range.
Carroll thought he had equalised in the 81st minute when Cech turned his headed effort onto the underside of the bar. However, referee Phil Dowd and his assistant deemed that the ball had not crossed the line.
The Reds continued to push forward in search of an equaliser, but their efforts were not rewarded following five minutes of stoppage time.