The Anfield club's captain scored three as Kenny Dalglish's side ended a run of three consecutive domestic defeats, while the Blues tasted defeat for the first time since January.
The Reds opened the scoring just past the 30 minute mark as Steven Gerrard placed the ball over Tim Howard in the Everton goal from the edge of the area, following good work from Martin Kelly.
Gerrard got the second five minutes after the restart, hammering in after good work down the right by Luis Suarez, and he secured his hat trick in injury time to become the first player to score three in the Liverpool derby for over 76 years.
Liverpool made four changes from the weekend defeat against Sunderland, with Sebastian Coates being replaced by Jamie Carragher in defense, Gerrard coming in for Charlie Adam, Dirk Kuyt dropping out for Stewart Downing and Andy Carroll starting in favor of Craig Bellamy.
With the upcoming FA Cup tie against Sunderland clearly in the back of David Moyes’ mind, Everton made six changes from the team that beat Tottenham. Nikica Jelavic, Tim Cahill, Phil Neville, Leon Osman, Royston Drenthe and Jonny Heitinga all took a place on the bench, with Denis Stracqualursi, Victor Anichebe, Tony Hibbert, Jack Rodwell, Steven Pienaar and Phil Jagielka taking their respective places.
It didn’t take long for the home side to assert some serious pressure on its visitor, as first Gerrard, and then Jordan Henderson went close inside the first seven minutes.
Gerrard burst into the penalty area before looking to slide the ball into the bottom far corner, but Howard got his left hand to it, and just when Henderson looked to smash the ball at goal, Rodwell threw himself in the way of the shot.
The match continued at break-neck speed as Everton went straight down the other end and almost opened the scoring itself. Leighton Baines marched down the left, beating Kelly before playing the ball through Henderson’s legs, but after cutting the ball back to Pienaar, the South African blasted over.
It was fairly clear that both teams were insistent on getting the ball down and playing, but it was the link-up play between Carroll and Suarez that made the next chance. The big striker did well to flick on a long ball to the Uruguayan with his head, but Howard saved well again.
Although the flow of chances slowed a little, after much back and forth, Liverpool took the lead through its captain just past the half-hour mark.
Kelly found space on the right and drilled a shot at Howard before attempting to pounce on the rebound, but the ball eventually came back to Gerrard on the edge of the area and he casually lofted the ball over the helpless Howard and into the back of the net.
Two minutes later Kelly was at it again as he got away from his markers down the left, getting on the end of a pass into the area, but his clipped effort went just wide of the far post. Stracqualursi then went close down the other end with a well-timed header, but Pepe Reina dealt with it and little else of note occurred as Liverpool went into the break 1-0 up.
However, it didn’t take long after the break for Liverpool to get its second, and it was Gerrard once again. Suarez did well down the right, getting down to the goal line, beating Sylvain Distin and fortuitously overrunning the ball into Gerrard’s path, where he smashed the it into the roof of the net.
Something similar almost happened again two minutes later on the other side of the goal as Suarez this time cut the ball back for Carroll, but the England international put his effort wide of the far post.
With half-an-hour left to find a way back into the match, Rodwell almost gave Everton a lifeline. Baines charged down the left and played a clever pass into the area for the midfielder, but his side-footed effort was stopped before it got to the goal by Jose Enrique who slid in and cleared at the last second.
Liverpool visibly took its foot off the proverbial pedal as the team suspected it had already done enough for the three points, but Everton wasn't giving up as Moyes threw on Drenthe, Jelavic and Osman.
The changes created more urgency in attack for the visiting side, but it was still struggling to create chances, with Rodwell's blocked effort from range the closest the team came to getting a goal back, and Liverpool soon got a third.
Gerrard broke through the center, charging down on the Everton penalty area before passing to Suarez to his left and receiving the ball back from the Uruguayan to knock into an empty net, securing the win.
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