This felt almost like a box-ticking exercise for a team as sublime as Manchester City. There was never any jeopardy against opponents with all the snarl and knowhow of a sleeping kitten. It was simply a case of getting the job done and moving on to the next one for City, who did not have to do much more than tickle Fulham’s tummy to return to the Premier League’s summit before Liverpool host Tottenham on Sunday afternoon.

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If there was a concern, it was that Sergio Agüero had to make way for Gabriel Jesus after complaining of a minor injury early in the second half.

Yet Pep Guardiola did not sound particularly worried when he said that City’s leading scorer went off only as a precautionary measure. Agüero, who will be assessed on Sunday, had already scored his 29th goal of the season by the time he took his seat on the bench and it spoke volumes that Guardiola devoted more time to discussing the weather, noting that it was strange to see the sun shining for the first time in seven months.

According to City’s manager, the warm conditions posed a genuine threat to his side’s chances of moving a point above Liverpool. Yet the champions barely had to break sweat to deal with Fulham, who must rank as one of the worst sides to grace the Premier League.

The gulf in class was captured by the Cottagers failing to muster a shot on target at home for the first time since 2010. Yet it would be unfair to dwell on Scott Parker becoming the first manager in their history to lose his first four matches. Parker inherited a mess from Claudio Ranieri last month and the west Londoners, who are 16 points below 17th-placed Burnley with six games left, have been destined to return to the Championship for a long time.

“I want the players to show what they can do,” Fulham’s caretaker manager said. “At times we have shown glimpses. It’s a tough season and I’ve been given the reins. It’s difficult.”

Fulham, timid and ineffective in their 5-4-1 system, had intended to frustrate Guardiola’s illustrious attack by staying tight and compact. The problem with that ploy, however, was that Parker’s players were riddled with anxiety even on the rare occasions when they had possession and City had to wait only five minutes to puncture the leakiest defence in the division.

Unable to cope with City’s high press, Fulham were punished for trying to play out from the back when Timothy Fosu-Mensah’s errant pass went to Kevin De Bruyne. Bad idea. De Bruyne, playing for the first time since 2 March after shaking off a hamstring injury, found Agüero, who looked right and saw Bernardo Silva. The Portugal midfielder cut inside and fizzed a crisp drive inside the right post from 20 yards.

“The way we started was amazing,” Guardiola said. “The first 15 minutes was incredible. We showed our focus. Seven games left for the Premier League, and it’s easy: we have to win every game to be champions.”

Fulham, bereft of belief, were horribly out of their depth in the face of such intensity and desire. They looked like crumbling every time City attacked and were fortunate not to concede a penalty when Fosu-Mensah, who had a shocking game in central defence, clattered into Raheem Sterling in the 30th minute.

Facebook Twitter Pinterest Bernardo Silva celebrates after giving Manchester City a 1-0 lead after five minutes. Photograph: Charlotte Wilson/Offside/Getty Images

Kevin Friend’s refusal to point to the spot was only a minor irritation for City given that they had doubled their lead three minutes earlier. Once again Fulham were punished for their sloppiness, Joe Bryan’s miscued pass giving the superb Silva the chance to free Agüero, who swept past the woeful Maxime Le Marchand before lifting a lovely shot over the advancing Sergio Rico.

Resigned to their fate, Fulham had no threat without the injured Aleksandar Mitrovic leading their attack. Even a protest about expensive ticket prices in the 55th minute lacked any real spark.

City might come to regret that their goal difference after an afternoon of total dominance is only eight better than Liverpool’s. De Bruyne scuffed straight at Rico after bursting through what passed for Fulham’s defence. Ilkay Gündogan whipped a venomous effort over. Sterling threatened with a bouncing effort.

Yet that was a minor quibble. City, who will be fresh when they host Cardiff on Wednesday, have thrown down the gauntlet and the pressure is on Liverpool to respond.