The turning point came at the start of the second half, but the question is whether it was Benitez's decision to make up for an earlier omission by sending on Xabi Alonso as substitute that transformed Liverpool's fortunes, or was it Zat Knight's freak own-goal in the 48th minute that got them back into the game?
Alonso certainly made a huge difference, giving Liverpool a creative fulcrum and also occupying the thoughts of Steed Malbranque, who had done most to get Fulham ahead. But it is questionable whether Liverpool would have made such a comprehensive comeback without a helping hand from Lady Luck, who intervened to transform a tame shot from Milan Baros into one of the strangest own goals of this or any other season.
The 25-yard effort from Baros looked to be heading towards the corner flag until it struck Knight, bounced down on to the ground and looped over Edwin van der Sar and into the net. The goal gave Liverpool the belief to go forward, and prompted by Alonso they scored a further three times, despite having Josemi sent off in the 76th minute for his second yellow card.
Yet Benitez was reluctant to put too much emphasis on the role played by Alonso, whose relegation to the subs' bench was thought to be linked to his wastefulness with free-kicks in Liverpool's recent defeats by Manchester United and Chelsea. Benitez was also some way off the mark when he suggested his side had dominated the opening 45 minutes. 'I thought we controlled the first half,' he said.
Chris Coleman saw it differently, choosing to pinpoint the way his side hit the panic button, and refused to curse his luck - or lack thereof. 'We are having a bit of bad luck but there is no point feeling sorry for ourselves or using it as an excuse to paper over the cracks.
'What disappoints me most is that our heads seem to drop too easily, and we did all the things in the second half that we should not have done. I don't know where the panic came from. For the first half we played with confidence and scored two good goals, but we can't seem to play consistently well for 90 minutes.'
Fulham certainly started with the determination of a team aware that a win would have lifted them above Liverpool and into mid-table. Boa Morte opened the scoring in the 23rd minute after a sloppy flick from Salif Diao was intercepted by Malbranque, who slipped a forward pass to Brian McBride. The American sent his shot towards the far corner, where Boa Morte slid in to put the ball over the line from close range.
Six minutes later it was 2-0 as Pembridge robbed Luis Garcia in the centre circle and the ball was flicked on by McBride to Malbranque. Again the Frenchman's forward pass was perfect, allowing Boa Morte to run on and hammer a low shot into the far corner.
So far so good, and, as Coleman said, his half-time message was 'more of the same'. But Liverpool's supporters had been calling for Alonso, and Benitez obliged, taking off the hapless Diao and seeing an instant return with Knight's bizarre own-goal. It gave Liverpool the spur they needed and they finally started to attack Fulham with conviction.
They equalised in the 70th minute when Baros scored a goal that was undoubtedly his. Alonso crossed from the left, Luis Garcia's glancing header was saved by Van der Sar, but Baros thumped the loose ball home from close range.
Josemi's dismissal, for a foul on Boa Morte, looked to have made their task harder, but it was Liverpool who scored next and again there was an element of luck. Papa Bouba Diop, back in the Fulham midfield after suspension, fouled Garcia 25 yards from goal. When Alonso tried to curl his free-kick over the defensive wall, Diop leapt high to head the ball but succeeded only in diverting it into the corner of the goal, leaving Van der Sar wrong-footed.
And when Igor Biscan sidefooted the ball home from 20 yards with only his second touch after being introduced as a stoppage-time substitute, Liverpool knew their luck was in - and Fulham's was all out.