Phil Foden and Erling Haaland struck inside the first 15 minutes as City extended their perfect start in the Premier League to six games
Messi, who recently left Paris Saint-Germain for Inter Miami, is in with a chance of succeeding Karim Benzema and winning the Ballon d'Or for the eighth time in his remarkable career after leading Argentina to World Cup glory in Qatar last year
The Norwegian's 52-goal campaign helped City win the treble of Champions League, Premier League and FA Cup in his first season at the club.
Julian Alvarez and Nathan Ake opened the scoring for the champions, who have beaten Fulham in their last 15 league meetings and now top the table with a perfect 12 points from four games. Fulham, who scored an early equaliser through Tim Ream before being overrun, have four points from their four games.
Norway striker Haaland scored 52 goals in 53 games to help City win the treble of Champions League, Premier League and FA Cup, while Bonmati inspired Spain to World Cup glory earlier this month.
"You should try and tape your mouth. I sleep with it. Doing a lot of things is not good but doing small things every single day for a longer period really pays off."
Haaland drove a first half spot-kick against the post before his header put City in front after the break at Bramall Lane
The trio emerged as the leading vote-getters from a jury comprised of coaches of clubs in UEFA competitions, those in charge of European national teams and a select group of journalists
Haaland, 22, has scored 36 goals in 35 games this season, breaking the previous record of 34 in a single Premier League campaign shared by Andy Cole and Alan Shearer that had stood for nearly three decades