Playing against one of his many former clubs, Crouch was bundled over by Liam Ridgewell for the penalty with which Steven Gerrard broke the deadlock five minutes from time, after releasing Boudewijn Zenden on the left and moving into the penalty area for the return. Gerrard tucked away the penalty and four minutes later, as self-belief drained out of Villa, Xabi Alonso drilled home a flattering second after Olof Mellberg had stretched to stop Crouch tapping in from close range.
Crouch should have scored with a free header from an earlier cross by Zenden and created a chance for Gerrard that Thomas Sorensen had to move swiftly to save, although it was the penalty incident that predictably divided managerial opinion. Ridgewell had his arms around Crouch when the pair crashed to the floor, yet the Liverpool player was possibly the first to resort to wrestling.
'I've got to watch what I say because these are precious people, but it was a terrible, terrible decision and the referee cost us the game,' David O'Leary said. 'We weren't just hanging on for a draw at that point we were looking for a winner. If anyone was hanging on it was Liverpool.'
Benitez was equally convinced the decision was fair. 'It was a clear penalty,' he said with a smile, doubtless relieved to have a first away win of the season under his belt without any of the usual hangover after a European game.
O'Leary had a point. Villa appeared to have soaked up all that Liverpool could throw at them by the 85th minute and were looking dangerous once Juan Pablo Angel joined Milan Baros in attack, but they reckoned without Crouch's subtle contribution. 'It's not all about his goalscoring,' Benitez said. 'He wins us the ball and he keeps possession. He gives us something different.'
This game certainly needed something different, for despite the presence of costly strikers such as Fernando Morientes, Djibril Cisse, Baros and Kevin Phillips, there was barely a sniff of a goal until Crouch lurched into his penalty area routine. Sorensen made a couple of good saves, most notably from Cisse in the first half when Gerrard's through-pass gave the £15million forward all the time in the world to come up with something more original and effective than blasting the ball straight at the goalkeeper, but until the closing minutes, Villa's only attacking plan seemed to be to wait for Liverpool to make a mistake.
The visiting team did their best to oblige and the ever-reliable Jamie Carragher came to the rescue on a couple of occasions, when Alonso and John Arne Riise surrendered possession in dangerous areas, but despite Liverpool's superiority in passing and movement, it was poor fare for the spectators until the first goal.
If Sky want people to pay to view any more games such as this, they should consider making Roy Keane an offer he cannot refuse to continue his career as a pundit. The Manchester United captain's observations on Harry Kewell's new hairdo would have been more entertaining than anything this match produced and Keane could also have brought to bear his withering opinions on questions such as whether Cisse offers more style than substance, where Gerrard and Alonso were supposed to be playing and whether Villa were actually aware the game had kicked off for the first half-hour.
To be fair to the much-maligned Kewell, he, too, was effective in the short time allotted to him. It was his cross that led to Liverpool's second goal, Zenden's that brought the first and Crouch was in the middle on both occasions. Liverpool's substitutions worked so well it made you wonder why Benitez bothered with Cisse, Morientes and Garcia in the first place. All three seem determined to save their best for Europe and their contributions here were negligible.
So the joke about Liverpool running out of ideas after 76 minutes - or whatever time Kewell takes the field next week - may have to be retired. The joke at Liverpool, in the league at least, is currently the starting line-up.