Maradona, a guest of Fulham at Craven Cottage, watched his Argentine compatriot Carlos Tevez score twice as City eased the pressure on manager Roberto Mancini.
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In Sunday's earlier game, Blackburn Rovers gave their new Indian owners an immediate return with a 2-0 victory over Aston Villa at Ewood Park.
Tevez struck first for City in the sixth minute and set up Yaya Toure for City's third after just 35 minutes. In between, another Argentine, Pablo Zabaleta, made it two, before Tevez provided the final flourish after half-time.
"It was a fantastic performance," Mancini told Sky Sports. "It is difficult to win (away from home). If we play like that, we can win everywhere."
City are on 25 points, three behind joint leaders Chelsea and Manchester United.
Chelsea lost 1-0 to Birmingham City on Saturday and United beat Wigan Athletic 2-0 at Old Trafford. Arsenal, in third on 26 points, lost 3-2 at home to Tottenham Hotspur.
Mancini's multi-million-pound squad had scored only three goals and taken five points from their last five matches to leave their fans frustrated with the Italian and his cautious style.
FIZZING SHOT
In west London against the team managed by his predecessor at City Mark Hughes, the club's expensive players showed their potential.
Tevez set the tone when he cleverly rolled defender Carlos Salcido to collect a pass from Gareth Barry and finish low past Mark Schwarzer.
Spaniard David Silva's low cross was cleared by Damien Duff into the path of Zabaleta, who drove a fizzing 20-metre shot past Schwarzer.
Toure then benefited from Tevez's neat pass, the Ivory Coast midfielder surging past a defender before drilling home from an angle.
Tevez enjoyed some luck for City's fourth in the 56th minute. Zabaleta's shot was heading for Schwarzer's hands before Tevez stuck out a foot and the ball looped over the bemused Australian keeper.
"I think it was the best we've played this year," Barry said. "We knew it was a good chance to make an impression today. We try not to worry about (the criticism) too much."
Fulham, whose consolation came from a deflected Zoltan Gera effort in the 70th minute, are fourth from bottom, clear of the relegation zone only on goal difference.
"City were excellent - credit to them and Mancini," Hughes said. "But we allowed it to happen. We lost belief after the first goal and needed to be more aggressive in closing them down. It was another wake-up call for us."
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