Andy Carroll inspired Liverpool's 2-0 win over 10-man Everton after Jack Rodwell was sent off in a controversial Merseyside derby at Goodison Park on Saturday.
David Moyes' side were forced to play with 10 men for more than an hour after Rodwell was harshly sent off by referee Martin Atkinson midway through the first half for a robust challenge on Luis Suarez.
Despite their numerical advantage Liverpool laboured to make the breakthrough and Tim Howard looked like being Everton's hero after denying Dirk Kuyt from the penalty spot at the end of the first half.
But Carroll's first goal in 10 league appearances in the 71st minute put Liverpool in control before Suarez made the game safe eight minutes from the end.
The last time Kenny Dalglish stood in the visitors dugout at Goodison Park as Liverpool manager was 20 years ago.
Two days after an epic FA Cup tie ended 4-4, an emotionally-drained and exhausted Dalglish announced he was quitting Anfield.
Back in the derby spotlight, Dalglish resisted temptation to start with Steven Gerrard, the England midfielder once again on the substitutes bench following his long lay-off with a groin injury.
However, Kuyt did earn a recall and it was the Netherlands international's excellent ninth minute cross which presented Suarez with the game's first real chance.
Suarez was unable to add to his league tally of three goals this season after heading straight at Howard before Everton responded immediately through Tim Cahill.
The Australian had scored five times in his previous 13 Merseyside derbies, but his hopes of a sixth goal were dashed when Pepe Reina tipped his header over the bar after Seamus Coleman had whipped in a cross.
Everton were beginning to settle and great foot-work by Sylvain Distin opened up the Liverpool defence before the French defender let fly with a powerful effort which flew narrowly over the bar.
Then came the moment which left Everton with 10 men. The Merseyside derby has proved one of the most volatile fixtures in the English calendar over recent seasons and Rodwell became the 20th player to be dismissed in Premier League encounters between the clubs, and the 11th in the last 14 games between the rivals.
It was harsh on Rodwell, who was given his marching orders after a challenge on Suarez that saw him win the ball.
The England under-21 international looked distraught as he walked off and the home side had every right to feel aggrieved.
But Everton could have few complaints when Atkinson pointed to the penalty spot after Phil Jagielka's needless challenge on Suarez two minutes before half time.
Liverpool, however, were unable to take advantage as Howard brilliantly kept out Kuyt's spot kick before Adam rattled the bar deep into first half stoppage time from 20 yards.
The visitors continued to crave out chances after the interval, Louis Saha clearing Carroll's header off the line in the 52nd minute.
Yet the game appeared to be drifting towards a stalemate when Liverpool broke the deadlock in the 71st minute.
Carroll has struggled to win over the doubters since his £35 million move from Newcastle in January.
But the England striker produced a quality finish from 12 yards after Jose Enrique's pull-back from the left.
And Everton's misery was complete when Leighton Baines and Distin got in a tangle to allow Suarez to pounce from close range to seal victory in the 82nd minute.