Manchester United may be first in the current pantheon of dislike at Anfield but any win over Everton carries special tribal significance. Particularly when Liverpool had to play 10 against 11 for nearly an hour and still managed a comfortable victory in the 203rd Merseyside derby.

Three goals against resurgent neighbours is a worthy tale for any Liverpool supporter and the fact that the team suffered the loss of Steven Gerrard due to an outbreak of rampant stupidity by the captain will be glossed over in the telling. Gerrard kicked the ball away to get one yellow card and then scythed down Kevin Kilbane just 35 seconds later to make sure referee Phil Dowd had little option but to send him off.

Instead of buckling at the loss of their "special one", however, Liverpool gained strength and an own goal from Phil Neville, and strikes from Luis Garcia and Harry Kewell gave them a deserved win. They have now scored 18 times in four games, which is not bad for a team who two weeks ago were being branded as a team who always fire blanks.

"I'm delighted with the players, for the supporters and with the final score," Rafael Benitez, the Liverpool manager, said. "It's not easy to play with 10 men but we controlled the game and were aware at set-pieces."

On Gerrard's dismissal, he came perilously close to criticising his captain. "You have to use your brain as well as play with your hearts," he said. "He is a player with a lot of passion but in derbies you also need to be calm. He made a mistake."

Everton, who also had a player dismissed when Andy van der Meyde led with an arm in an aerial challenge with Xabi Alonso, got a goal back through Tim Cahill but have won just one of their last 13 derbies. "We didn't play well, especially after they went down to 10 men," David Moyes, their manager, said. "We're all disappointed we didn't show what we can do."

As Moyes intimated, the watershed in a game of 11 yellow and two red cards was Gerrard's dismissal. Before it Everton were the better team and could have scored twice by the ninth minute - Cahill turned and shot too tamely after Leon Osman had pushed the ball into his path and the Australian also found the side netting from James Beattie's head on. After it, their numerical superiority coincided with creeping mediocrity and the first half descended into an unedifying morass of inaccurate passing and wild lunges until Liverpool took the lead in stoppage time.

Give a Liverpool fan the choice of a perfect goal and, if it is not Jamie Carragher beating six players en route, then a former Manchester United player in an Everton shirt heading past his own goalkeeper will do nicely thank you. Neville, duly obliged, racing to the near post to meet Alsonso's corner with a flick that diverted the ball over Richard Wright into the far corner.

Liverpool did not deserve to be ahead 1-0 and they certainly did not merit a two-goal lead, but within two minutes of the restart they had secured this advantage, this time with a move that summed up the qualities of Benitez's side. Everton had been straining to contain Peter Crouch in the air all afternoon and had done so only because the referee had allowed them to foul the beanpole striker at will.

He got first to a long ball and his touch had the added virtue of not only releasing Garcia but of drawing Richard Wright from his line. The Liverpool striker got there first and was able to lob the Everton goalkeeper into the empty net.

Everton looked like men finding their nightmares coming real and Moyes was about to make a triple substitution when they scored unexpectedly in the 61st minute. Osman's corner was accurate enough but it hardly merited Liverpool's defenders gawping at it like it was a thing of beauty and while they stared, Cahill jumped to head in.

That put the Everton substitution plan on hold for seven minutes, although when it did happen it hardly had the desired effect because within five minutes they too were down to 10 men. Moyes said that Van der Meyde's guilt as he challenged with Alonso was dependent on the angle, but from which ever way you look at it, the injury-prone Dutchman is threatening to become a liability at Goodison rather than an asset.

On numerically level terms again, Liverpool were the more likely to prosper and with six minutes remaining Kewell sealed the victory with the best goal of the game. Twenty yards out, with little or no run-up he summoned power and accuracy to fire a shot over Wright into the roof of the net.

It was a unfittingly skilful moment for game high on spite and low on ability. Not that Liverpool will care.