Germany winger Sane tapped home after 96 seconds and David Silva netted his 50th Premier League goal midway through the first half.
Raheem Sterling helped himself to a third goal this season as City made a similarly rapid start to the second period – Fulham's cavalier attacking approach leaving their excellent goalkeeper Marcus Bettinelli repeatedly exposed.
Fernandinho pounced on a dreadful pass from Jean Michael Seri and drove forward, greeting Sane's return by gifting him a simple finish.
Bernardo Silva dazzled with sublime close control before playing in Sterling – a combination of Bettinelli and his crossbar denying the England winger.
Sterling and Bernardo Silva were both involved when David Silva crashed via the underside of the bar in the 21st minute.
Ederson beat away a couple of Andre Schurrle strikes as Fulham retained their attacking intent, but the visitors were indebted to stunning Bettinelli stops from Sterling and Sane before half-time.
Sergio Aguero crossed as Sterling crowned a lightning break 98 seconds into the second half and the Argentina striker soon made way for Gabriel Jesus, who almost scored with his first touch.
There was more wayward finishing from the Brazil striker as City's forwards queued up to get in on the act, with Bernardo Silva blazing over in the 81st minute to miss out on the goal his wonderful efforts merited.
What it means: Timely boost for Sane
Since being named PFA Young Player of the Season last term, Sane's existence has been a turbulent one. A shock omission from Germany's World Cup squad, the 22-year-old was recalled for international duty despite failing to make City's starting XI in four Premier League games. He left Joachim Low's squad early for the birth of his daughter, but not before Toni Kroos publicly questioned his attitude. Guardiola defended Sane ahead of this match and the breakthrough goal settled him into an accomplished showing.
Pat on the back: Polished showing from Bernardo Silva
There is no shortage of prime attacking talent in this City side, but Portugal star Bernardo Silva was in irresistible form as his inventive playmaking, clever movement and velvet touch led Fulham a merry dance.
Boot up the backside: Sorry stuff from Seri
Fulham's commitment to attack might have panned out very differently had Seri not set their downfall in motion with his second-minute gift. The Ivory Coast midfielder chased shadows thereafter, making those links to Barcelona seem a distant memory.
Key Opta stats
- Courtesy of this victory, Manchester City have won six consecutive Premier League matches against a single London team for the first time.
- Fulham have registered their second worst start to a Premier League campaign after five games (4pts, -5 goal difference); only bettering 2011/12 (3 pts, -3 goal difference).
- Manchester City are unbeaten in the Premier League against newly promoted sides in their last 34 home meetings (W30 D4), since losing to Reading 0-2 in 2007.
- Fulham have won none of their last 10 Premier League meetings with reigning champions, drawing two and losing eight.
- Leroy Sane has had a hand in 18 goals in his last 16 Premier League games at the Etihad Stadium (6 goals, 12 assists).
- Sane’s opener for Manchester City was the quickest goal in the Premier League this season so far, at one minute 36 seconds.
City were able to wind down in preparation for their opening Champions League match at home to Lyon, with a more combative encounter no doubt in prospect at Cardiff City next weekend. Fulham must respond at home to in-form Watford.