Sterling opened the scoring for City on Saturday with a clinical finish as he ended a run of six games in all competitions without a goal.
De Bruyne added a second from the penalty spot after Sterling had been clumsily brought down by Fulham's Joachim Andersen.
The Cottagers failed to really test Ederson in the City goal as they managed just a solitary attempt on target in a one-sided contest.
City imposed themselves from the kick-off and Sterling drew a fine near-post save from Fulham goalkeeper Alphonse Areola in the third minute.
Guardiola's side were ahead shortly after when Sterling latched on to a slick pass from De Bruyne before he calmly slotted the ball past Areola.
Fulham tried to soak up City's pressure but Scott Parker's tactical plan was in tatters when Andersen upended Sterling in the box as the forward won the 20th Premier League penalty of his career – more than any other player.
De Bruyne, who missed his last penalty against Liverpool, stepped up and sent Areola the wrong way with a confident spot-kick.
14 - Kevin De Bruyne has made 14 assists in the Premier League in 2020; the most of any player in the competition, and more than twice as many as any other Manchester City player. Unstoppable.— OptaJoe (@OptaJoe) December 5, 2020
A brief mix-up between Ederson and John Stones on the half-hour saw both players breathe a sigh of relief after the latter's backpass rolled wide of the goal with the City keeper off his line.
It was a brief moment of respite for Fulham and Areola was soon called upon again at the other end of the pitch to keep out a Sterling volley.
De Bruyne continued to provide the impetus for City's attacks after the interval and struck the crossbar after he combined well with Gabriel Jesus.
City went into cruise control for the remainder of the game, although Ivan Cavaleiro briefly flickered into life for Fulham when he cut inside and saw a speculative effort saved by Ederson.
Ruben Dias had the best of City's late chances when he met De Bruyne's deep cross at the back post but could not direct his effort on target.
What does it mean?
After a patchy start to their Premier League campaign City have now strung together back-to-back wins in the competition for the first time this season.
It gave Guardiola victory in the 700th game of his managerial career as his City side swaggered to the kind of dominant win that has become his signature. If this was a portent of what is to come, City will be firmly in the title reckoning.
Determined De Bruyne oozes class
Since he joined City, De Bruyne has both scored and assisted in a Premier League game 16 times - no player has done so more in that time (level with Liverpool's Mohamed Salah).
The Belgium international was at his creative best against the Cottagers, always in pockets of space and looking for a pass to open up the Fulham defence. De Bruyne had more shots and made more tackles (both six) than any other City player. His 55 passes came with an accuracy of 83.6 per cent
Aina exposed as the weakest link
This was a game that Fulham defender Ola Aina, on-loan from Torino, will not remember in a hurry after City's players rang rings around him.
He could not lay a glove on Sterling and De Bruyne as he made just two tackles in the whole contest. The Nigerian also lost possession 13 times with just one interception. A tame long-range shot that dribbled out for a goal kick summed up a miserable display.
Key Opta Facts
- City are unbeaten in their last 16 meetings with Fulham in all competitions (W13 D3), winning the last 10 in a row by an aggregate score of 29-3.
- Fulham have conceded more goals than any other Premier League side this season (21), with no side conceding in more different games than the Cottagers (10).
- City have scored as many goals over their last two Premier League games as they had in their previous seven in the competition (7).
- De Bruyne has been involved in more shots than any other Premier League player this season (62 – 34 shots, 28 chances created), with the Belgian involved in eight against Fulham this afternoon (6 shots, 2 chances created).
Fulham are in domestic action a week on Sunday when champions Liverpool are the visitors to Craven Cottage.