Mohamed Salah helped Liverpool back to the top of the Premier League with a goal that came 14 seconds after Fulham had an effort controversially disallowed for offside.
Replays showed the decision on Aleksandar Mitrovic's header was borderline with Liverpool left-back Andrew Robertson appearing to be in line with the Serbia forward.
But as the Fulham players celebrated, Liverpool goalkeeper Alisson initiated a lightening counter attack that Salah, who ran unopposed from halfway, fully capitalised on.
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.
Up until Salah's goal it had been tough going for the hosts who started well but were then frustrated by a well-marshalled Fulham side who remain bottom of the division.
Slavisa Jokanovic's team had arrived at Anfield with the worst defensive record in the division but with on-loan Sevilla goalkeeper Sergio Rico also impressing, they kept the hosts at bay for long periods and also created several promising chances.
Ryan Sessegnon and Mitrovic both spurned good opportunities to score while the teams were level.
But once ahead, Liverpool - who have an unenviable record against the bottom three Premier League clubs under Jurgen Klopp - rarely looked like relinquishing their advantage as they consigned the visitors to a sixth consecutive league defeat.
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 the Fulham offside trap to open the scoring.
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 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.