The Citizens were made to work for maximum points at the Etihad Stadium as they fell behind just before the hour mark when ex-Manchester United man Andreas Pereira poked Fulham into the lead.
However, Mateo Kovacic restored parity for the hosts just six minutes later before netting his second less than two minutes into the second half to turn the contest on its head - the Croatian's first club double in over a decade.
Marco Silva's men impressed throughout and went close to levelling on a few occasions, but City increased their advantage eight minutes from time when substitute Jeremy Doku cut inside from the left and fired a thunderous strike beyond Bernd Leno.
Rodrigo Muniz gave Fulham hope of a late comeback with an 88th-minute goal, but the reigning Premier League champions held on to claim all three points and extend their unbeaten run at the start of the 2024-25 campaign to 11 games in all competitions.
Pep Guardiola's side remain second in the top-flight table, level on points with third-placed Arsenal, while Liverpool enter the international break one point clear of both teams at the summit after seven matches played.
Man City machine keeps on going
Victory for Man City has seen them extend their remarkable winning run against Fulham to 17 matches across all competitions - the longest winning run one team has had over another in English football league history.
This run includes 13 consecutive Premier League victories in which they have scored 42 goals and conceded just eight, keeping eight clean sheets in the process. They have also won two FA Cup ties by an aggregate score of 8-1 and one EFL Cup fixture (2-0) during this impressive run.
Meanwhile, Man City have also equalled their longest ever unbeaten run in the Premier League, with success over Fulham extending this streak to 30 matches.
It equals the Citizens' previous record run between April 2017 and January 2018, and is also the joint-fourth longest unbeaten run in Premier League history, with Arsenal's 49 games without defeat between May 2003 and October 2004 ranked the best ever to date.
Man City have won 24 of the 30 games during this run, scoring a total of 77 goals, and they will have the opportunity to break their unbeaten club record run in the Premier League when they travel to Wolverhampton Wanderers on October 20.
In addition, Man City have also extended their impressive unbeaten record at the Etihad to 50 games in all competitions - their last defeat on home soil was against Brentford in November 2022.
Kovacic: 'We showed great character in tough Fulham game'
Reacting to Man City's win over Fulham, Man of the Match Kovacic told reporters: "It was a tough game, like every game here in the Premier League. There is no easy game in the league.
"I think we dominated in the beginning and could have scored. We then conceded and then came back quickly.
"In the end we won it. It was a tough game against an opposition in good form, so for us it is good to continue on a winning form. It is never easy to play in the Premier League and today we showed great character. Good game for us.
"The manager told us (midfielders) we should be around the box because we're always there. Today we pushed.
"Luckily I was there, Bernardo gave me a great ball, in the end it was a good control and a good shot. So it was important as always that we win. It means a lot because my wife is pregnant so it was great to get some goals for the little one.
"It doesn't matter who scores, the most important are the three points and hopefully now we can continue like this."
Man City have a favourable-looking run of fixtures in the Premier League coming up after the international break, with a trip to Wolves followed by encounters with Southampton and Bournemouth.