Raheem Sterling wrapped up the points once and for all with another goal at the start of the second half, and City's stranglehold over the game only strengthened as they cruised to the victory.
Pep Guardiola made four changes to his side, including a first Premier League start of the season for Sane, and the out-of-favour Germany international took just 97 seconds to make his impact.
It proved to be an ominous snapshot of what was to come as City broke through almost at will throughout the first half, with the impressive Bernardo Silva and Sergio Aguero both firing tame efforts on goal.
Fulham were architects of their own downfall to a certain extent, with their gung-ho approach to the game playing right into Man City's hands, and the hosts were inches away from doubling their advantage after only 15 minutes when Sterling was played clean through on goal, only to see his low effort bounce off the leg of Marcus Bettinelli and up against the crossbar.
The visitors' refused to abandon their attacking philosophy despite the obvious perils, and they also played their part in an entertaining contest with Andre Schurrle their most dangerous player and firing an effort over the crossbar before City's second.
The two-goal cushion finally arrived midway through the first half - by which point it was already thoroughly deserved - as Silva put the finishing touch to a fluid team move, slamming home from close range for his 50th Premier League goal.
Still Fulham did not alter their gameplan, and they offered enough going forward to suggest that a two-goal lead may not be enough, with Schurrle again the most likely culprit when his disguised effort was parried away by the keeper on the half-hour mark.
City were soon back on the front foot, though, and Aguero should have done better when he got his head to a pinpoint aerial pass into the box by Silva.
Schurrle kept Ederson busy with another sharp strike from the edge of the area which needed to be tipped over, but City were back up the other end in a heartbeat and Sane almost doubled his personal tally moments later when his shot was denied by Bettinelli.
Sterling was the next to come close at the end of the first half as he waltzed into the area before seeing his shot saved by the keeper, and from the resulting corner the home side did have the ball in the back of the net once again - only for Sane's flick to be correctly ruled out for offside.
The two-goal margin flattered Fulham at half time, but City wasted no time in making the scoreline more representative of their utter dominance with a goal almost immediately after the restart.
Having taken the lead 97 seconds into the first half, their third arrived 98 seconds after the interval when Sterling tapped home a simple finish from close range after Aguero had made it impossible to miss with a low ball across the face of goal.
Bernardo was thwarted when trying to cap his man-of-the-match display with a goal when he saw his effort blocked moments later, and it quickly became clear that Fulham had made no changes to their approach during the interval.
There was a blow for City when Aguero limped off ahead of the beginning of their Champions League campaign, but his replacement Gabriel Jesus almost made an immediate impact, firing off target with his first touch after being found by Silva.
Fernandinho almost got in on the act with a fiercely-struck shot which zipped inches past the post with Bettinelli beaten, and the Brazilian midfielder then combined with Sterling to set up Jesus, who again could not find the target.
City were able to drop down a gear without surrendering any of their control over the game, and they continued to create chances too with Sterling and Jesus both failing to hit the target.
The hosts' best chance of a fourth goal came nine minutes from time when Jesus latched on to Kyle Walker's pass before teeing up Bernardo, who lacked composure despite being unmarked and blazed his effort well over when he should have done better.
It wasn't until the 89th minute that Fulham had their first meaningful shot of the second half when Floyd Ayite cut inside before dragging his finish wide, and they even forced Ederson into a save in stoppage time as Aleksandar Mitrovic was denied a consolation.
The Cottagers were eventually put out of their misery, though, with the final scoreline flattering Slavisa Jokanovic's side on a day which saw them completely outclassed by the champions.
City will now turn their attention to a Champions League tie with Lyon, whereas Fulham will look to return to winning ways at home to Watford next weekend.
MAN CITY (4-3-3): Ederson; Walker, Otamendi, Laporte, Delph (Gundogan 67'); Bernardo, Fernandinho, Silva; Sterling (Mahrez 74'), Aguero (Jesus 54'), Sane
FULHAM (4-3-3): Bettinelli; Christie, Odoi, Mawson, Sessegnon; Seri (Zambo Anguissa 56'), McDonald, Johansen; Vietto (Ayite 69'), Mitrovic, Schurrle