Liverpool toiled in growing frustration in the 205th Merseyside derby, but they could not find a way past Alan Stubbs and his team-mates, who added a point to the three they claimed back in September from a 3-0 home victory.
• Stubbs hails Everton's progress
Everton took the gamble of playing Andrew Johnson up front, despite only a fortnight of treatment on what was thought to be a serious ankle injury.
He passed a late fitness test, while Tony Hibbert returned at full-back for the Toffees for the first time since October after a groin injury.
Liverpool boss Rafael Benitez opted to play all three of his main strikers - Peter Crouch, Dirk Kuyt and Craig Bellamy - while leaving out Sami Hyypia and going with a central defence of Jamie Carragher and Daniel Agger.
At times it left Liverpool looking lopsided, with no width on the left where Mikel Arteta did a good job in halting the runs of John Arne Riise.
With fog rolling in across a packed and rocking stadium, Everton were the first to show real intent. Tim Cahill and Mikel Arteta on the right worked space and possession, and Liverpool struggled to cope with the supply of crosses.
Xabi Alonso nervously prodded one low centre behind, adding to Steven Gerrard's general annoyance with the standard of defending, before Hibbert motored onto a ball on the edge of the box to crash a fierce drive into Jose Reina's chest.
There were few real chances in the first period, but Tim Howard produced an excellent reflex save with his feet to block a Crouch hook, before Bellamy got in on the left to take a return ball and fire past Howard, only to be rightly given offside.
Leon Osman was booked on 10 minutes for a foul on Jermaine Pennant and when Pennant's cross was nodded on by Kuyt, Bellamy just failed to connect with a header as the ball bounced wide of a post.
Everton were doing a decent job of containing Liverpool's attacking threat with their extra man in midfield.
Arteta, in particular, showed strength and skill on the right, while Stubbs and Joleon Lescott were coping with the aerial threat of Crouch.
It was not until the 25th minute that Liverpool created another chance, Howard saving well from Kuyt at full stretch, while Alonso saw a 20-yard dipping effort just clear the bar.
Liverpool's back line were being harassed into mistakes and poor distribution. Benitez was pleading for better passing from Alonso and a quicker delivery to Pennant. This must have encouraged Everton, because they knew they were halting the accurate flow of Liverpool's attacks.
Liverpool came out for the second period with more intent, Alonso fired a 25-yard shot straight at Howard, and Carragher had a close-range effort blocked by Phil Neville.
Neville was never far from Gerrard, a constant annoyance to his fellow captain, and his marshalling of Everton's midfield was outstanding.
All the Toffees' toil was nearly rewarded on 60 minutes when Steve Finnan gave the ball away to Johnson, who cut into the box and pulled the ball away from the covering Alonso to force Reina into an excellent and crucial save from 12 yards
Joseph Yobo outpaced Bellamy on a long run onto an Alonso pass, and despite increased tempo and more urgency, Liverpool were continually frustrated.
But the pressure was mounting. Gerrard sent a dipping 20-yard free-kick inches wide, before Arteta was booked for a foul on Riise on 67 minutes.
On 72 minutes Neville was booked for a foul on Bellamy as Everton were forced back leaving Johnson isolated up front.
Kuyt was thwarted by a Lee Carsley tackle and then delayed too long after being set up by Bellamy. Liverpool just could not find the space and time in the box to make their possession tell.
After 80 minutes Johnson, who had chased everything diligently all game, was replaced by Victor Anichebe.
Five minutes later the hard-grafting Bellamy was replaced by Robbie Fowler for what will almost certainly be his last taste of a Mersey derby.
Crouch failed to connect after a neat Fowler touch-on from a Carragher ball into the box.
Riise headed a deflected Arteta corner off the line as Everton made a rare appearance in Liverpool's box.
Stubbs hails Everton's progress
Man of the match Alan Stubbs hailed the 'massive progress' at Everton after
a goalless draw at Anfield ensured an unbeaten season against local rivals
Liverpool.
Having beaten their nearest neighbours 3-0 at Goodison Park in September,
Everton produced a highly-creditable performance against the odds at Anfield.
There were few chances, but despite Liverpool's constant possession and
second-half onslaught, they were denied a crucial three points in their quest
for second spot in the Premiership.
'It's a fantastic result,' central defender Stubbs told Sky Sports Prem
Plus.
'We knew they were going to come at us from early on, especially after the
last derby. It was a hard shift for the boys in midfield and us at the back but
it's a fantastic result for us.
'It was always going to be a battle. The lads deserve a lot of credit.
'It shows massive progress. We're unbeaten against them this season and it's
a long time since we've been able to say that. It is something we have got to
build on.'
Captain Phil Neville, who also produced an heroic performance, added: 'It's
midfield where the battles are won and we wanted to get in their faces, not give
them time on the ball. In the past we've rolled over but we didn't today.
'The back four were magnificent.'
Toffees chief David Moyes picked out his captain and veteran defender for
special praise.
'We've played them twice now and not conceded, so all credit to the
defenders.
'We've seen what Chelsea had to put up with when they came here, Liverpool
are a really good side.
'They (Stubbs and Neville) are two very popular lads in the dressing room and
they both put in excellent performances today. Stubbs' experience shone
through.'
Rafael Benitez was frustrated by Everton's defensive approach.
'I'm really disappointed. One team wanted to win and one didn't want to lose
but we tried to keep going forward and creating chances.
'When you play against eight players behind the ball, narrow and deep, you
cannot create many clear chances. You just keep trying. You cannot say anything
about this.'
Asked about the impending arrival of Javier Mascherano subject to Premier
League clearance, Benitez told Sky Sports Prem Plus: 'I don't have any idea. We
are waiting. With confidence, but waiting.'
Benitez also hopes the proposed takeover of the club is completed soon.
'If it's next week it will be better, then we can start talking again about
football.'
Liverpool 0 - 0 Everton
