Lucas Leiva grabbed Liverpool's winner as the Anfield side saw off the challenge of League One side Crewe.
Daniel Agger put the Reds ahead when he drove in a free-kick awarded for Michael O'Connor's foul on David Ngog.
O'Connor atoned for his foul as he shot home from close range after keeper Diego Cavalieri parried Calvin Zola's header from a Billy Jones corner.
But Leiva timed a run to perfection to meet a Jermaine Pennant cross and headed in to wrap up a Reds win.
Liverpool manager Rafael Benitez introduced Fernando Torres after Lucas' goal and the striker was immediately involved.
Pennant had been constant menace for the Reds down the right flank and he crossed for Torres, whose header was tipped past the post by Steve Collis.
The Crewe keeper saved again from the Spaniard two minutes later after Torres had broke clear of the Crewe defence.
Liverpool were given a late scare when Tom Pope slid in to meet a low cross but put his effort wide.
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Goals: Agger 15, Leiva Lucas 58.
Goals: O'Connor 25.
Att: 28,591
Ref: Michael Oliver (Northumberland).
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