Striker Dirk Kuyt's 50th Liverpool goal gave his side a 1-0 victory in a fiery 213th Merseyside derby at Anfield which saw both teams reduced to 10 men.
The Dutchman scored for the fourth time in as many games with a close-range header 10 minutes after half-time.
Liverpool played the last 55 minutes at a numerical disadvantage after Sotirios Kyrgiakos was dismissed for a two-footed challenge on Marouane Fellaini, while Steven Pienaar was shown a second yellow in second-half injury time.
The red cards took the tally to 19 in the last 13 years but referee Martin Atkinson somehow missed Marouane Fellaini's stamp on the Greek defender's right shin in the same incident which led to his red card.
It threatened to overshadow a fiercely-contested encounter until Kuyt struck early in the second half to ensure Everton's winless run at Anfield since 1999 continued.
Liverpool have now gone seven Barclays Premier League matches without defeat, keeping six clean sheets in the process.
By contrast, Everton's nine-match unbeaten run came to an end. The last team to beat them before today had been Liverpool at Goodison in late November and they have now won just two of the last 21 league derbies.
The tone for the match was set in the opening 15 seconds with Jamie Carragher's strong but fair challenge on Pienaar which left the South Africa midfielder rolling on the ground holding his shoulder.
Unfortunately, it was only to get worse in the first half as Atkinson's leniency saw a number of over-the-top tackles escape the required action.
Fellaini, competing for the ball, kicked Kuyt in the face as the Dutchman lay on the ground without censure, while Pienaar was only cautioned for a challenge which started at Javier Mascherano's right knee and worked its way down.
Carragher went into the book for going through the back of Pienaar in retaliation while the other booking of the first half went to Kuyt for tripping Landon Donovan.
In between all the flying tackles there was very little football played in the opening 45 minutes.
Steven Gerrard's inswinging fourth-minute free-kick forced Tim Howard to punch out from under his own crossbar while Daniel Agger, on his first appearance for nearly a month, fired a right-foot shot a couple of yards over from a corner.
David Ngog fired a shot well wide after Maxi Rodriguez and Gerrard had combined while late in the half the Liverpool captain rattled Howard's crossbar with a 25-yard free-kick.
For Everton, Leighton Baines' left-footed free-kick was tipped over by Jose Reina while Tim Cahill directed a free header over from seven yards in added time.
Liverpool began the second half well and Ngog saw an early left-foot shot deflected wide by Sylvain Distin.
And they were rewarded in the 55th minute when Kuyt, despite being clung onto by Phil Neville, nodded in Gerrard's inswinging corner from three yards with Howard left flapping.
Johnny Heitinga's foul on Rodriguez earned him a booking but Gerrard hit the free-kick straight at Howard.
In the 63rd minute Ngog was replaced by Ryan Babel, who was given a rare outing in his preferred position up front.
Everton manager David Moyes sent on Aiyegbeni Yakubu and Victor Anichebe for Saha and Leon Osman in an attempt to find the equaliser.
A scuffle broke out seven minutes from time when Gerrard caught Pienaar after clearing the ball and bizarrely Atkinson, having not blown for a foul, booked the Liverpool captain and then Anichebe for his part in the retaliation.
Liverpool were content to defend their lead and counter-attack when possible but Reina had to be alert to tip behind Yakubu's shot on the turn.
In the fifth minute of added time Pienaar was sent off after jumping into Gerrard as the hosts hung on to maintain their momentum going into an equally-important match at Arsenal on Wednesday.