The victory was City's seventh in a row in the league, while Fulham have now lost each of their last eight in the top flight to remain in 19th position, still 13 points from the safety of 17th spot.
Without 10-goal leading scorer Aleksandar Mitrovic through injury, Fulham's starting XI had managed just seven Premier League goals between them during the 2018-19 campaign ahead of kickoff in the English capital.
City's first half-chance of the match arrived in the fifth minute when Aguero found space inside the penalty box, but Cyrus Christie was on hand to make a smart block.
Less than one minute later, though, the breakthrough arrived. A sloppy pass from Fosu-Mensah saw Fulham concede possession in midfield and Bernardo Silva picked out the bottom corner with a beautiful curling effort.
Sergio Rico had to tip a dipping De Bruyne effort over the crossbar in the ninth minute as City continued to force the issue, before Sterling had an effort deflected wide moments later.
Fulham were struggling to escape their own penalty box let alone their own half in the first 15 minutes as Sterling had another goal-bound strike blocked, before De Bruyne fired straight at Rico after breaking into a one-on-one situation.
The home side finally had an opportunity in the 19th minute when Cairney picked out the head of Babel from a free kick, but the Netherlands international saw his effort fly wide of the post.
Normal service was resumed shortly after, though, and City doubled their lead in the 27th minute when Aguero expertly picked out the far corner with a chipped effort.
Fulham were again the architects of their own downfall, though, with a poor pass from Joe Bryan releasing Bernardo Silva, who played in Aguero to score the away side's second of the afternoon.
The hosts were having their moments down the other end and Ederson had to palm clear a low drive from Sessegnon, but City looked capable of scoring every time that they broke past the half-way line.
City's first shot of the second period came from Nicolas Otamendi in the 53rd minute, but the Argentine almost cleared the stadium with his strike.
Fulham actually made the better start to the second half as they threatened in the wide positions, while City lost Aguero in the 57th minute as the Argentine limped off to be replaced by Gabriel Jesus.
Rico had to keep out a powerful strike from Sterling just past the hour as the visitors threatened a third, but there was not the same intensity about Guardiola's side in the second period.
Both managers took the chance to use their bench as the match developed, with Andre Schurrle and Neeskens Kebano joining the play for Fulham, who were not out of the match heading into the final 20 minutes.
Kebano then had a half-chance for Fulham in the 83rd minute, but the substitute headed wide of the post from close range, before Ederson gathered a deflected free kick from Schurrle.
City had opportunities to add to the scoring late on, but there is no question that the English champions were conserving energy in the second period ahead of a busy run of matches.
Next up for City is a home game against Cardiff City on Wednesday night, while Fulham's search for a victory will continue away to Watford on Tuesday.
FULHAM (5-2-3): Rico; Fosu-Mensah, Chambers, Le Marchand, Christie, Bryan; Anguissa, Cairney (Schurrle 70'); Sessegnon, Babel (McDonald 88'), Ayite (Kebano 64')
MANCHESTER CITY (4-3-3): Ederson; Walker, Otamendi, Laporte, Zinchenko; De Bruyne (Fernardinho 75'), Gundogan, D Silva; B Silva, Aguero (Jesus 57'), Sterling (Mahrez 88')