Barca were looking for an instant return to form in their European opener after falling to a surprise loss on Saturday at the hands of Getafe in La Liga, and they could not have asked for a happier evening as the Hungarian side were put to the sword at Camp Nou.
Lionel Messi struck first for his side after 27 minutes, converting from the penalty spot after being felled himself in the area to curtail a typically explosive dribble.
The stage was then set for Fati to shine, with the 17-year-old doubling his side's lead just before the half-time whistle.
While Fati did not manage perfect contact on the volley from Frenkie de Jong's cross, it was good enough to wrong-foot Ferencvaros goalkeeper Denes Dibusz and put Barca 2-0 ahead.
As well as establishing a comfortable cushion for Ronald Koeman's charges, the strike also claimed a new record for the youngster.
It was his second goal in the Champions League for Barcelona, making him the first ever player under the age of 18 to score more than once in the European competition.
His maiden strike came in the 2019-20 edition, when he netted what proved to be the Catalans' winner in a 2-1 defeat of Inter in December 2019.
Since making his debut in August last year Fati has collected an astonishing number of records. He now stands as Barcelona's second-youngest debutant and goalscorer in La Liga and the youngest player to do either in the Champions League for the club, as well as holding the distinction of being the youngest player ever to score twice in a Liga match for any club.
Following his goal, Fati turned provider with a neat backheel to play in Philippe Coutinho for Barca's third of the evening against Ferencvaros.
A red card for Gerard Pique and subsequent penalty for the Hungarians, converted by Igor Kharatin, reduced the deficit to 3-1, leaving the 10-man hosts to see out the final minutes at a numerical disadvantage.
That did not seem to slow them down, though, with another 17-year-old later finding his name on the scoresheet.
The new signing from Las Palmas made it 4-1 after coming off the bench for Fati - one month his senior - making further history as the pair became the first U-18s to both score in a single Champions League match, while Ousmane Dembele added a fifth in the final minutes to complete the rout for Barca.