A Jack Rodwell red card reduces Everton to 10 men, as Liverpool take the points in the Merseyside match.
Carroll and Suarez score as controversial sending off overshadows derby
Andy Carroll's first Barclays Premier League goal of the season and another from Luis Suarez gave Liverpool victory in a controversial 216th Merseyside derby against 10-man Everton at Goodison Park.
The hosts had Jack Rodwell sent off in the 23rd-minute for a sliding tackle which did not appear to be dangerous but despite the disadvantage they matched their near-neighbours for long periods.
Dirk Kuyt saw his first-half penalty brilliantly saved by Tim Howard but 19 minutes from time Carroll powered home Jose Enrique's cross and Suarez sealed victory.
Everton striker Lois Saha made his first start of the season and midfielder Tim Cahill was passed fit.
The Frenchman's appearance in the line-up, two weeks after voicing his frustration on Twitter after failing to make the squad against Wigan, meant captain Phil Neville was relegated to the bench in the only change from the defeat at Manchester City.
Liverpool midfielder Jordan Henderson was dropped for the first time after starting all six Barclays Premier League matches this season as manager Kenny Dalglish opted for the experience of Dirk Kuyt, scorer of six derby goals.
Marouane Fellaini's shot was deflected wide in the third minute to give Everton the first corner of the match but Leighton Baines' cross was claimed at the second attempt by Jose Reina in a crowded six-yard box.
Liverpool's first real threat to the hosts' goal came in the ninth minute when Kuyt chased down Phil Jagielka and crossed for Luis Suarez but the Uruguay international could only direct a weak close-range header straight at Tim Howard.
Cahill produced a much better effort as Everton launched an immediate counter-attack as his header was tipped over by Reina at full stretch.
The home side continued to press and Sylvain Distin cut inside Jose Enrique, one of five derby debutants in the Liverpool side, and blasted a left-footed shot just over.
But just when everything appeared to be going in Everton's favour their luck changed in controversial fashion.
Jack Rodwell slid in to challenge Suarez and although seemingly winning the ball with a tackle which did not appear to be dangerous, referee Martin Atkinson immediately brandished a red card.
It was the 20th dismissal in 39 Barclays Premier League meetings, 13 of which have been Everton players with eight of those coming in the last 10 games at Goodison.
The momentum of play changed in an instant as Cahill, who had been posing a threat to the Liverpool defence in an advanced role behind Saha, was dropped back into a left-sided midfield role.
Everton's high-tempo pressing play was abandoned for a deeper-lying, more measured approach and that played into the visitors' hands as they were able to control possession of the ball.
However, they looked like they would not be able to break through until Phil Jagielka brought down Suarez on the corner of the penalty area a minute before half-time and Atkinson pointed to the spot.
Kuyt stepped up but Howard saved brilliantly low to his left.
In added time Charlie Adam did beat Howard but his 25-yard shot cannoned back off the crossbar.
Everton continued to make light of their reduced number after the break with Saha shooting just wide after being teed up by Cahill just inside the area.
But Liverpool were starting to create more openings and Andy Carroll's header looked to be creeping inside the post from Stewart Downing's corner before Saha hacked away.
Another Carroll effort had Howard scrambling to his left to turn around the post while Kuyt deflected Adam's quickly-taken free-kick wide.
Seamus Coleman made way for Royston Drenthe just before the hour but it was Saha who was next to threaten, rifling a 25-yard shot just wide of Reina's right-hand post.
Steven Gerrard and Craig Bellamy were both introduced in the 67th minute for Adam and Downing.
But it was not the talismanic Reds captain who made the difference but his fellow substitute.
Just four minutes after coming on the Wales international's run down the left released Jose Enrique and Kuyt cleverly ducked under the Spaniard's cross to allow Carroll to power home from eight yards.
The match was wrapped up in the 82nd minute when Suarez, whom Everton fans had vilified as a cheat for his minimal role in Rodwell's sending off, grabbed the second.
Collecting Kuyt's knockdown he was lucky to have Distin's clearance bounce into his chest but he made the most of it to place a left-footed shot past Howard from six yards.
The striker's celebrations in front of the Gwladys Street end were interrupted by a number of bottles being thrown onto the pitch.
However, it could not dampen celebrations on the red half of Merseyside as Kuyt almost made it 3-0 when he hit the post in added time.