Aguero drove home his 19th goal of the season from the penalty spot, then set up strike partner Edin Dzeko with some unselfish work after half-time.
Between them, the pair have scored 35 times this season, making a mockery of recent assertions that the pair have difficulty operating in tandem.
And with Chris Baird turning Adam Johnson's cross into his own net, City were not hindered by the wintry conditions that even left the fans to chant for the end long before the five minutes' injury-time had been completed.
The old cliche of there being no easy games in the Premier League could have been made for a day like this.
In theory, 30 points clear of their visitors and boasting a 100% record on home soil this term, it should have been a straightforward assignment.
Yet significant questions were asked of City before kick-off.
In sub-zero temperatures and with snow getting increasingly heavy, the Blues were without skipper Vincent Kompany due to a knee injury, on a run of just three wins from their last nine games, and facing a team who had lost on just one of their eight visits to this stadium and battled back to draw at Craven Cottage in September despite being two goals down.
The evidence of the opening stages suggested it was going to be one of those difficult evenings, with Fulham intent on keeping their defences tight and relying on the predatory instincts of Clint Dempsey.
City needed a helping hand, and referee Mike Dean provided it.
Fooled completely by Johnson initiating contact with Baird inside the box, Dean pointed to the spot when a yellow card for the City man could easily have been the correct decision.
Aguero, five matches without a goal - his worst run since joining City - converted to the corner despite the returning Mark Schwarzer going the right way.
Fate had not finished for City.
For when Aguero flicked Aleksandar Kolarov's cross into the path of Johnson, Baird got in the way as the winger turned it back towards the danger area, giving Schwarzer no chance of keeping it out.
Now the damage was done, which meant it did not matter much that Schwarzer's lightning reactions prevented Philippe Senderos scoring a second own goal, nor that David Silva got a legitimate penalty after he had his legs taken away by City old boy Dickson Etuhu.
Aside from Damien Duff's angled drive, Fulham offered little and the game would have been over had it not been for the bravery of Brede Hangeland, who threw himself in the way of a goalbound Edin Dzeko strike.
The value of City's first-half efforts were not fully apparent until the second had reached its midway stage, with the snow becoming steadily heavier.
Twice Dean had to stop play for the lines to be swept, Senderos was booked for crashing into Kolarov with a tackle that owed something of its recklessness to the underfoot conditions, and neither side could get any flow into their game.
Baird had a free-kick gathered by Joe Hart, who has been mentioned in some quarters as a potential England skipper for Euro 2012 following John Terry's demotion.
With defending proving increasingly difficult, Aguero's nimble feet carried him into the area and past two half-hearted attempts at tackles.
It was a measure of the striker's awareness that instead of going for goal himself, he rolled the ball to an unmarked Dzeko, who finished with ease.
After a spate of disciplinary problems, City got away with one when Kolarov, about to be booked for hauling back Mousa Dembele, became engaged in a head-to-head duel with the Fulham man.
Dembele was booked but Kolarov escaped with a lecture in addition to the yellow card he would have received anyway.
The visitors hit the post when a cross-shot from substitute Bryan Ruiz flicked off Dzeko and then the woodwork before rolling to safety.
But the goalmouth action was over, the last notable moment coming when Mancini introduced transfer-window arrival David Pizarro for his debut in the final minute.