Sane, making his first league start for Guardiola’s side this term, netted after one minute and 36 seconds as the defending champions maintained their unbeaten start to the season.
David Silva doubled the hosts’ lead before the break, with Raheem Sterling all but securing the win two minutes into the second half.
A fourth win in five games keeps City within touching distance of league leaders Liverpool and Chelsea, who have taken maximum points so far.
Guardiola said he was impressed by 22-year-old Sane’s performance at Etihad Stadium, having restricted the Germany international to substitute appearances before the international break.
“We never had doubts about Leroy’s quality,” said the Spaniard. “He shows us many times in the last season and today he played again so good.
“We cannot forget sometimes this kind of thing happens, he is 21, 22. Sometimes he has to realise what, like a professional, he has to do.
“I am delighted for his performance and so confident.”
City were rarely troubled by the newly promoted Cottagers, restricting the visitors to handful of half chances at Etihad Stadium.
The hosts, perhaps with one eye on Wednesday’s Champions League opener against Lyon, eased off the pace in the second half but could have added to their lead with a number of opportunities falling to substitute Gabriel Jesus.
Sane enjoyed a glittering season as Manchester City won the title last term, scoring 10 goals and proving one of Guardiola’s main attacking outlets, but he has been restricted to a spot on the bench so far this campaign.
It took the winger, who also surprisingly missed out on a place in Germany’s World Cup squad in the summer, less than two minutes to find the net on his return.
The hosts punished Fulham’s Jean Michael Seri for giving the ball away in midfield as Fernandinho broke forward and teed up 22-year-old Sane inside the six-yard-box.
It was the quickest Premier League goal of the season so far and the culmination of a good few days for Sane, who said after the game he became a father this week.
City’s only dropped points this season came at newly promoted Wolves but, having not lost at home to a promoted team in 11 years, they were always in complete control against Fulham and doubled the lead on 20 minutes.
Bernardo Silva’s good work down the left was eventually finished off by David Silva’s half volley that struck the bar on its way in – it was the Spaniard’s 50th Premier League goal, becoming the fifth City player to reach that landmark after Sergio Aguero, Yaya Toure, Carlos Tevez and Edin Dzeko.
Sterling had also hit the bar in the first half as he and Sane caused problems out wide, but the England forward got his reward for a strong performance within two minutes of the restart as he tapped in from Aguero’s low cross.
BBC
