An eventful derby has a selection of everything with a red card, missed penalty and two goals as Kenny Dalglish makes first visit to Goodison Park since returning to Anfield
The scoreline could have been worse for home side had Dirk Kuyt converted a penalty kick late in the first half.
The early dismissal of Rodwell forced a rethink for Everton and for much of the contest the hosts were in the game as Liverpool couldn't press its advantage but the two goals from the Liverpool strike force finally sealed the game.
It was Liverpool had the first of many early chances to open the ledger when a delicious ball from Dutchman Kuyt to Luis Suarez was squandered as Suarez headed tamely into the palms of the camouflaged clad Tim Howard.
Seconds later an Everton counter resulted in header extraordinaire, Tim Cahill, forcing a fingertip save from Pepe Reina to redirect the effort over the bar.
The early excitement subdued until the fuse was well and truly lit when Martin Atkinson dismissed Jack Rodwell when the youngster slid in on Suarez. It seemed a questionable decision at first sight with the replays not supporting the official’s decision.
Rodwell was furious with the outcome and was seen lashing out at objects on the bench as he made his way to the dressing room whilst David Moyes was hurriedly formulating a new plan with his coaches.
The Uruguayan reinforced his position as public enemy number one as he was fouled by Phil Jagielka late in the first half to give Liverpool a penalty, but there was no question about this infringement.
Dirk Kuyt stepped up to take the spot-kick as Goodison Park held its breath, only to release a raucous cheer moments later as a diving low save to the left from Tim Howard kept the scores level.
Liverpool did have one last chance to score before the interval with a long range shot from Charlie Adam smashing into the crossbar.
Second-half substitute Craig Bellamy made a swift impact on the game when his pass to the overlapping Enrique allowed him to break for the byeline and deliver a cross to Carroll who finally broke the resistance of Howard and break the game open.
Liverpool sniffed blood in the air and continued to play the ball wide to make the ten men of Everton chase in the unseasonably warm weather and as Everton tired, sloppy defending let Suarez have not one, but two bites of the cherry and he made them pay with his persistence leading to the second goal.
There was no way back now for Everton and Liverpool contently kept hold of the ball and allowed the time to expire.
Moyes would have found it difficult to take many positives from the game but Tim Howard's efforts will not go unnoticed as he was the standout player.
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