Just moments after being brought on against Inter on Tuesday with the scores locked at 1-1, Fati found the bottom left corner with a powerful driven effort.
In the process, Fati broke a record previously held by Peter Ofori-Quaye, who scored for Olympiacos aged 17 years and 194 days in 1997.
Ernesto Valverde's side were in need of a spark at the San Siro and got it in the form of Fati.
After the Catalans opened the scoring through Carles Perez, Inter equalised just before half-time through Romelu Lukaku with Lautaro Martinez then finding the back of the net twice in the second half, only to be denied both times for offside.
Fati was then introduced for Barcelona in the 85th minute and just a minute later he'd settle the contest after a sharp one-two at the top of the box with Luis Suarez was followed by a pin-point finish.
That record-breaking strike would prove decisive as the Catalans claimed a 2-1 victory to deny Antonio Conte's side progression to the knockout stage.
Barcelona finished top of Group F having won four and drawn two of their six matches, while Inter ended third, three points shy of Borussia Dortmund.
Fati's goal continues his breakout season for Barcelona. After making his debut in August, he became the club's youngest scorer after striking in the same month against Osasuna in La Liga.
In September, the Spain U21 international then made his Champions League debut, becoming the Catalans' youngest player to feature in the competition.
Having turned heads around the world, Barcelona recently locked Fati down to a contract extension running until 2022 with a release clause of €170m (£144m/$188m).
"La Masía is for me the best school in the world," Fati said at the time. "They helped me in everything from the first day I arrived and I am very grateful to the people who work there. Everyone is spectacular.
"From the first day, I learned a lot from everyone. Also in difficult times, because they have always been there to support me.
"From now on I have to continue working more than ever to be able to have opportunities and continue enjoying. Everything else will come."
While Fati's playing minutes have been reduced over the past month, his father recently ruled out the possibility of a loan move in January.