City missed chances to record a bigger margin of victory, but will be pleased to come through another 90 minutes with little incident or injury.
Just as last weekend against Burnley, City were ahead with only a few minutes on the clock.
It is the scenario all visiting teams fear as containment and game plans go out of the window and it was Sterling who did the damage.
Kevin De Bruyne burst forward through the middle before playing a perfectly-weighted pass to Sterling who confidently slotted a low right-foot shot past the keeper and into the bottom left corner to end his six-game run without scoring.
Fulham kept City out for another 20 minutes, but when the lead was doubled, it was the same combination from the opener that did the damage.
Joao Cancelo fed Sterling who took the ball into the box, checked back inside and as he did, Joachim Andersen clipped his knee giving referee Jon Moss a simple decision in pointing to the spot.
De Bruyne may have missed his last effort against Liverpool, but he made no mistake with this one, sending the keeper the wrong way to put City 2-0 up.
The visitors were almost gifted a goal just past the half-hour as John Stones mopped up a Fulham attack and played the ball back towards Ederson – only the City No.1 had raced out and for a moment, it looked like the ball might end up in the back of his net, but it instead rolled wide for a corner.
City almost made it three just five minutes after the restart with a breakaway move that saw De Bruyne feed Jesus in space inside the box – he cut inside a challenge before teeing up De Bruyne who saw his shot strike the crossbar.
And De Bruyne will feel he should have scored again, when City again broke forward with Riyad Mahrez’s exquisite touch and through ball sending the captain clear but Areola saved well – and it wasn’t his first decent stop of the game.
Credit to Fulham for staying in a game that could have ended with a more damaging loss in a game where they competed well, if threatened Ederson’s goal rarely.
Raheem Sterling scored one goal and won the spot-kick for the other, as well as being busy and a threar throughout.
City easing though the gears
Much has been made of City’s start to the 2020/21 Premier League season, but this victory – at least for a time – meant Pep Guardiola’s side were just three points off the top for at least a few hours.
It means that, for all the games that haven’t panned out our way earlier in the campaign, City have not lost any ground and are in the thick of this title race – albeit at a very early stage.
Goals are starting to come, too – though there will be disappointment the margin of victory wasn’t greater against Fulham with the shots ratio still high compared with the chances converted.
What it means
City move up to fourth in the Premier League table ahead of Leicester City – though with several games yet to be played this weekend, it is likely that will change.
John Stones reaction
"We said after the Champions League game that we wanted to keep another clean sheet. Today was a tough opponent that we did a few days work on after the game in Porto and we knew what we were up against.
"We said it from the start that we want to keep the wins going. There could have been more, In every game we play, we could score more - we’re frustrated with ourselves - but we’re happy with the three points. It’s something we can learn from ahead of the next game we go into.
"It’s always the same [competition for places]. The manager demands a lot from us and expects a lot from us. When there’s a chance, we’ve got to take it. It’s a healthy competition.
"We know what’s expected of us. If we don’t deliver then we know someone else is fighting for that spot. That’s served us well over recent years. Everyone has high standards and keeps them there and that’s what the manager wants.
"It’s another step forward, another chance to put a mark on this season. We take it game by game and see where it takes us. We focus on each game and we got three points. I could say before the game everyone’s words worked and that transpired onto the pitch. We’ve got to keep this winning mentality going in every game we play."
On no subs used:
“The guys who didn’t play will play Wednesday. I decided to play 90 minutes with these guys and a fresh 90 minutes for others.
“We want to try to continue to win games.”
“Raheem always tries. I have no doubts, for a striker it’s always important to score goals and that’s what he’s done, so it’s good.
On the Manchester derby:
“Yeah, of course in the Champions League we have done the job but we will respect the competition - Marseille and Olympiakos play for Europa League.
“After this game we will see about United and how we want to play. We want to be there until the end, win games. To win the Premier League you have to win a lot of games.”
City complete the Group C Champions League group stage schedule with a home game against Marseille on Wednesday (8pm).
We have already won the group, while Marseille can still qualify for the Europa League if they can finish above Olympiakos – both teams have three points.
Then, it is the Manchester derby at Old Trafford next Saturday (5.30pm kick-off).
Fulham: Areola, Aina, Andersen, Adarabioyo, Robinson, Zambo, Reed (Lemina 68), Reid (Kamara 71), Loftus-Cheek, Lookman, Ivan Cavaleiro.
Subs: Mitrovic, Cairney, Rodak, Ream, Bryan
Stats and facts
Raheem Sterling has now won more penalties (20) than any other player in Premier League history.
City have recorded back-to-back Premier League wins for the first time this season.
This was Pep Guardiola's 250th game in charge of City - and his 700th as a manager.
City have now kept four successive clean sheets in all competitions.
This was City's tenth win in a row against Fulham (all comps).