Liverpool took command of the game early when a Gerrard header sent Crouch clear after 11 minutes. The England international calmly rounded Nigel Martyn to score his sixth goal in his last six starts.
It was 2-0 after 18 minutes after an Everton header fell to Gerrard on the edge of the box. Gerrard hammered the ball home and Martyn was left stranded after the ball took a slight deflection off Joseph Yobo.
Liverpool then seemed to take their foot off the gas and allowed Everton back into the game. Beattie scored for Everton around the half hour mark but the goal was ruled out when the linesman judged the ball to have gone out for a goal kick before it was crossed into the box.
That should have been a wake up call for the Reds but they didn't heed it and their impressive defensive record was breached on 42 minutes when James Beattie headed past Pepe Reina after good work from Kevin Kilbane and Simon Davies.
The goal prevented Reina from breaking Elisha Scott's record of eight successive clean sheets in the league that had stood since 1923. Reina will just have to make do with an equal share in the 82 year old record.
Any chances of an Everton comeback were wiped out within two minutes of the second half when Djibril Cisse broke clear, skipped past David Weir and buried a delightful shot past Martyn.
Things only got worse for the Blues when Phil Neville was dismissed for two bookable offences after 68 minutes. The sending off ended the game as a contest and Rafa Benitez was again able to make changes and give a rest to Gerrard, Crouch and Harry Kewell.
Everton finished the game with nine men when Mikael Arteta was sent off at the death, also for two bookable offences.