The 16-year-old came off the bench at half-time at El Sadar and made it 1-1 six minutes later, burying Carles Perez's cross with a fine header.
It was an historic moment for Fati, who last week became the second-youngest player to appear for Barca in the top flight when he came on for Perez in the 5-2 defeat of Real Betis at Camp Nou.
Fati takes the record as Barca's youngest scorer from Bojan Krkic, who wrote on Twitter: "It's always a great joy to see boys from the Masia enjoying and achieving their dreams. Congratulations for your record, Ansu!"
Only former Malaga forward Fabrice Olinga and Athletic Bilbao star Iker Munian were younger when they scored for the first time in LaLiga.
Born in Guinea-Bissau, Ansu arrived at Barca in 2013 at the age of 10 and recently signed a contract that will keep him at the club until June 2022.
After his outing against Betis, his father told RAC1: "I have seen him make his debut for Barca; I can die happily. It will not be the first time; there will be many more appearances."