Michael Owen grabbed an early 21st birthday present with the extra-time goal which put Liverpool on their way to the Worthington Cup semi-finals.
First Division leaders Fulham stretched Liverpool to the limit during normal time but the home side wrapped up the game when Vladimir Smicer and Nick Barmby bagged further goals in the final minutes of extra-time.
After 90 minutes without a goal - Danny Murhpy went closest when his curling free kick hit a post - Fulham put on Luis Boa Morte and Andrejs Stolcers for the extra half hour, but it was an early turn, run and shot from Owen that forced Taylor into a fingertip save that first threatened to break the ice.
Nick Barmby was next into the fray after 100 minutes, taking over for a struggling Heskey who had clearly picked up a muscle injury.
On 104 minutes, a succession of passes in the box, all in the air and all hasty, ended with Smicer having a glorious chance to break the deadlock, but his lob was off target.
Westerveld had to pull off a despairing flick over to stop a Stolcers' corner from swerving into the top corner.
Owen eventually managed the breakthrough when he fired in at the second attempt his first header being blocked on the line by Andy Melville after a Smicer cross from the right, seconds before the extra time break.
Liverpool grabbed their second with eight minutes remaining; Barmby racing away down the right before pulling the ball back for Smicer to place his shot high into the net.
Gerrard limped off with cramp before the re-start with Gary McAllister taking over.
Barmby then raced away to belt in the third in the dying seconds to give the scoreline a flattering look for Liverpool.
l Wimbledon coach Stewart Robson refused to criticise his beleaguered squad after they had only managed a 2-2 draw at home to Grimsby - but said his team's home performances deserved the boos ringing down from the terraces.
He said: ''I'm not going to criticise the team because they displayed a lot of heart and commitment and simply could not convert their chances. Football supporters are entitled to their own opinions and our home form deserves those boos from certain sections of the terraces.
''We may not play in front of big crowds but we have a number of loyal fans, who deserve better performances at home.''
Robson, covering for manager Terry Burton who was absent to undergo a minor operation, denied claims that poor performances were affecting his team's morale and results at Selhurst Park.
He added: ''For the first 15 minutes and for the warm-up it is difficult to motivate yourself in front of a small crowd but after that it makes no difference.
''The players have not got a mental block when they play at home but a win would do the team a world of good. We are a decent team and this is proved by our away record. We have the second best set of results in the league on our travels and can beat teams such as Birmingham, who were second in the league when we won there on Saturday.''
Elsewhere, Huddersfield manager Lou Macari admitted he has been taken by surprise by the speed of his side's revival after the 3-1 win at Nottingham Forest. Two goals from Kevin Gallen and a third in two matches for on-loan striker Peter Ndlovu saw Town climb off the bottom of Division One with a third successive win. Macari said: ''I thought it might take us a month or six weeks to get off the bottom if we were going to get off the bottom at all.'
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