Match ends, Liverpool 2, Fulham 0.
Fulham manager Slavisa Jokanovic said referee Paul Tierney showed "disrespect" to his team after disallowing a header from Aleksandar Mitrovic, which allowed Mohamed Salah to score 14 seconds later for Liverpool.
Replays showed the decision for Mitrovic's effort was a borderline call, with Liverpool left-back Andrew Robertson appearing to be in line with the Serbia forward.
The decision angered Jokanovic, whose team remain bottom of the Premier League after their sixth successive defeat.
"When I check the clips now it's Robertson (who) hasn't done a good enough job to squeeze up and my player is onside and scored the goal," he said.
"In one moment, a crucial moment, instead of 1-0 up we're 1-0 down.
"We can talk about this situation for hours, but the damage is done. It's a completely absurd situation to defend.
"In this country normally you cannot show disrespect to the referee and this is a problem because it's shown disrespect to my team, myself and Fulham supporters."
Salah's goal came after goalkeeper Alisson initiated a lightening counter attack, with the Egyptian running unopposed from the halfway line to open the scoring.
"We were a bit lucky and maybe because of Robbo it is not 100% offside because of his heel," said Liverpool manager Jurgen Klopp.
Xherdan Shaqiri's cushioned finish in the second half confirmed victory for the Reds who equalled their best start to a Premier League season, which came in 2002-03.
Liverpool and Salah approaching their best?
Klopp has maintained his Liverpool team are not yet at their free-flowing best - and that in itself should swell confidence around Anfield.
This victory ensured the Reds remain unbeaten after 12 league outings, eight points better off than at the same time last term and well placed to challenge for the league title.
Last season Liverpool toiled against the bottom three, drawing twice against West Brom, once against Stoke and losing at Swansea.
But Salah, who has now scored five goals and provided five assists in 633 minutes against newly promoted teams, helped to ensure the outcome of this fixture was not in question.
The Egyptian had scored nine times at the same stage last term but his performance against Fulham, where he registered his sixth goal of the campaign, suggested he is not far from replicating his best form.
The 26-year-old instigated a glorious early exchange with Roberto Firmino to carve the visitors' defence apart, only to see Rico react well to save at his feet.
And that was a precursor to what was to follow, with Rico again saving from the Egyptian before he broke clear to open the scoring.
"The most important thing is reacting quick in that situation and it was brilliant: Alisson, Trent (Alexander-Arnold), Mo and done," Klopp added.
Revised style sees Fulham improve
Fulham, whose expansive style of play proved so successful in the Championship last season, have yet to deliver results against clubs in the Premier League.
The Cottagers, who spent more than £100m on players in the summer, arrived at Anfield with the worst defensive record in the league, having conceded 29 goals from their opening 11 fixtures.
That prompted Jokanovic into a rethink as he deployed four central defenders in a revised system and fended off pre-match questions about his team selection.
And after early teething problems - with Sadio Mane firing wide from Trent Alexander-Arnold's cross - Fulham grew into the game.
Happy to concede possession and sit deep, the visitors could have delivered the perfect riposte of a goal when Ryan Sessegnon was sent clear by Mitrovic's flick-on.
The England under-21 winger, who covered more ground (12.22km) than any other player during the course of the afternoon, guided his shot wide of the right-hand post.
German forward Andre Schurrle then tested Alisson and Mitrovic failed to connect properly with a shot from 10 yards out.
When the Serbia forward powered a header past Alisson from Tom Cairney's cross it appeared as though Jokanovic's strategy might yield an unlikely dividend.
Instead the visitors, who managed the same number of shots on target as Liverpool in the first half, were undone by a moment of naivety with Denis Odoi's attempt to catch Salah offside.
Man of the match - Mohamed Salah (Liverpool)
Fulham close unwanted Barnsley record - the stats
- Liverpool have picked up 30 points from their opening 12 Premier League games (W9 D3 L0) - their joint-best total at this stage in the competition (level with 2002-03).
- Fulham have conceded 31 goals from their first 12 league games this season; only Barnsley in 1997-98 conceded more goals at this stage of a Premier League campaign (35).
- Fulham have taken one point from their past 19 Premier League games against the 'big six' sides (W0 D1 L18), losing all four games this season by an aggregate score of 2-13.
- Liverpool have won all nine home Premier League games under Jurgen Klopp against newly promoted teams, scoring 27 goals and conceding just three.
- Liverpool have kept 10 clean sheets in 14 Premier League games at Anfield in 2018; as many as they'd kept in the past calendar year (10 clean sheets in 21 home league games).
- Xherdan Shaqiri has either scored or assisted in five of his past six games for Liverpool in all competitions (two goals, three assists).
Liverpool travel to Watford for their next Premier League fixture on Saturday, 24 November (15:00 GMT) while Fulham host Southampton on the same day (15:00).
- 12GomezBooked at 77mins
- 4van Dijk
- 5WijnaldumSubstituted forHendersonat 69'minutes
- 3FabinhoSubstituted forKeitaat 90+2'minutes
- 23ShaqiriSubstituted forMilnerat 81'minutes
- 20Le Marchand
- 29Zambo AnguissaSubstituted forJohansenat 84'minutes
- 5ChambersBooked at 59mins
- 14SchürrleSubstituted forViettoat 78'minutes
- 10CairneySubstituted forSeriat 63'minutes
- 3R Sessegnon
- Paul Tierney
- Shots on Target
Second Half ends, Liverpool 2, Fulham 0.
Foul by Jordan Henderson (Liverpool).
Jean Michael Seri (Fulham) wins a free kick in the defensive half.
Substitution, Liverpool. Naby Keita replaces Fabinho.
Attempt blocked. Mohamed Salah (Liverpool) left footed shot from the right side of the box is blocked. Assisted by Sadio Mané.
Attempt saved. Roberto Firmino (Liverpool) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by James Milner.
Corner, Liverpool. Conceded by Stefan Johansen.
Corner, Liverpool. Conceded by Maxime Le Marchand.
Sadio Mané (Liverpool) wins a free kick in the attacking half.
Foul by Calum Chambers (Fulham).
Attempt missed. Aleksandar Mitrovic (Fulham) left footed shot from outside the box is high and wide to the left. Assisted by Cyrus Christie.
Hand ball by Maxime Le Marchand (Fulham).
Substitution, Fulham. Stefan Johansen replaces André-Frank Zambo Anguissa.
Corner, Fulham. Conceded by Joseph Gomez.
Substitution, Liverpool. James Milner replaces Xherdan Shaqiri.
Attempt missed. Trent Alexander-Arnold (Liverpool) right footed shot from outside the box is too high. Assisted by Roberto Firmino.
Substitution, Fulham. Luciano Vietto replaces André Schürrle.
Joseph Gomez (Liverpool) is shown the yellow card.
Foul by Joseph Gomez (Liverpool).