Pep Guardiola's team have had a patchy start to the season but are now just three points behind leaders Tottenham after a dominant display at the Etihad.
Earlier, Dominic Calvert-Lewin scored his 11th Premier League goal of the season to rescue a point for Everton in a 1-1 draw against struggling Burnley.
There were no fans at either match but West Ham were preparing to welcome 2,000 supporters to the London Stadium for the visit of Manchester United, with the same number due at Chelsea's match against Leeds.
City, who had won just four of their opening nine matches, are showing ominous signs they are returning to their best form after building on their 5-0 mauling of Burnley last week.
They made a superb start at the Etihad, with Raheem Sterling putting them ahead inside five minutes to end his recent goal drought.
The England forward, who had already had one shot saved by Alphonse Areola, raced through on goal from a measured Kevin De Bruyne pass and calmly side-footed into the far corner.
De Bruyne, in Guardiola's 700th game as a manager, doubled the lead from the penalty spot after Sterling was brought down by Joachim Andersen.
The Belgian rattled the bar early in the second half as City continued to dominate possession but they could not add to their lead.
The result lifts City to fourth in the table on 18 points, ahead of Leicester on goal difference, while Fulham remain fourth from bottom.
Earlier, Carlo Ancelotti's Everton trailed at Turf Moor after a fine strike by midfielder Robbie Brady before England forward Calvert-Lewin levelled on the stroke of half-time.
But neither side could find a winner in a contest in which goalkeepers Jordan Pickford and Nick Pope -- rivals for the England number one shirt -- caught the eye.
"We are not satisfied with the result but the performance was quite good," Ancelotti told the BBC. "The start was terrible and Burnley are able to defend. We created some good chances."
"(England manager) Gareth Southgate has to be pleased, both goalkeepers did really well," he added.
Premier League chiefs on Saturday issued advice to supporters on coronavirus safety measures, including a warning for fans not to get carried away when their team scores a goal.
"Fans can celebrate but should remain socially distanced from people outside their social bubble," said the advice.
"Hugging of other fans and high-fives should be avoided and fans are asked to be respectful to those around them, including avoiding excessive shouting or singing."
London and Liverpool are among the areas to have been placed into the Tier-2 category based on Covid-19 rates, meaning up to 2,000 fans will be able to attend matches.
But clubs based in Tier-3 areas, such as Manchester and Birmingham, are still not allowed to open their gates.
Manchester United will be keen to bounce back from their disappointing 3-1 defeat to Paris Saint-Germain this week, which left their Champions League hopes hanging in the balance.
United, who have won eight consecutive league games away from home, face a tough task against in-form West Ham, who have beaten United at home for the past two seasons.
Chelsea boss Frank Lampard goes toe to toe with Marcelo Bielsa in the late Saturday kick-off in the first league meeting between the bitter rivals for 16 years.
Leaders Tottenham and Liverpool, who are both on 21 points, are in action on Sunday.