TWO sendings-off followed by two Dirk Kuyt penalties wrecked Everton's hopes of taking the 206th Mereyside derby.
An incident-packed match was going the way of the home side at half-time as Everton led through a Sami Hyypia own goal.
But Tony Hibbert was sent off after he brought down Steven Gerrard early in the second half and Phil Neville followed for his injury-time handball that kept out a shot from Brazilian substitute Lucas.
Kuyt sent the ball to Tim Howard's left on both occasions to give Liverpool the three points.
Liverpool ran the show in the first 10 minutes and Yossi Benayoun, who got a bit of early joy on the left, set up the game's first chance for Andriy Voronin, who shot straight at Howard.
But once Everton managed to get a foothold in the game it soon became the tight, tetchy and often frantic affair that characterises so many Merseyside derbies.
Not helping the cause was the lack of creativity from midfield. With Neville and Phil Jagielka facing Momo Sissoko and Javier Mascherano in the centre there was plenty of fight but not much finesse.
But when they did manage to get the ball out wide, this looked like both sides' best outlet for making something happen and Leon Osman almost did when he skinned Hyypia and floated a dangerous chip that Pepe Reina had to desperately claw away.
This led to one of a series of set-pieces that Everton forced at regular intervals during the first half and this always looked their best hope of breaking the deadlock as they gradually began to get into the ascendancy.
And this proved to be the case after 38 minutes when Everton took the lead from a corner. It fell to Alan Stubbs on the right side of the box and he did brilliantly to dig out a cross that was flicked on by Joleon Lescott then sliced into his own net via the post by a bemused Hyypia.
With Lescott getting an alarming amount of space down the left, Everton sensed Liverpool were there for the taking and the England defender's cross was dragged narrowly wide by Osman before half-time.
Everton also started the second half piling on the pressure but it was from one of their own corners that the game took a turn for the worse for them as they lost both a player and the lead in the 52nd minute.
Voronin did well to follow up Benayoun's clearance and release Gerrard, who was tugged back by Hibbert as he closed in on goal. Gerrard went flying in the area to seal Hibbert's red card for a professional foul and Everton's misery was compounded when Kuyt tucked away the penalty.
John Arne Riise then blazed over a great chance to give Liverpool the lead as they tried to expose the extra gaps left by Hibbert's dismissal, although the outstanding Phil Neville moved back at right-back to retain the shape of Everton's back four.
And they almost regained the lead at the other end when Yakubu's half-volley from 25 yards almost crept inside the post.
Further sights of goal were wasted by Voronin (twice), Sissoko and Ryan Babel as Liverpool pressed for a late winner - and it arrived in injury time when Neville had no choice but to palm away Lucas's goalbound effort as he followed up Howard's save from Kuyt.
The Dutchman did the rest.
Everton finished the game complaining to Clattenburg that they should have had a last ditch penalty themselves for a foul on Lescott by Jamie Carragher. The official was booed off after being surrounded by home players.
EVERTON: Howard; Hibbert, Stubbs, Yobo, Lescott; Arteta, Jagielka, Neville, Osman; Anichebe (Baines 84), Yakubu (McFadden 78). Subs: Wessels. BOOKED: McFadden. SENT OFF: Hibbert, Neville.
LIVERPOOL: Reina; Finnan, Hyypia, Carragher, Riise; Gerrard (Lucas 72), Mascherano, Sissoko (Pennant 88), Benayoun (Babel 69); Kuyt, Voronin. Subs: Crouch, Itandje. BOOKED: Kuyt, Carragher.
REFEREE: Mark Clattenberg