The 16-year-old marked his sixth successive start in all competitions with the game's opening goal in the 14th minute, meeting Joao Cancelo's cross to tap home from just a few yards out at the back post.
Richard Sanchez equalised for Granada on the stroke of half time before Manchester United loanee Facundo Pellistri put the visitors in front with a close-range finish on the hour mark.
Two goals were then netted just six minutes later, with Robert Lewandowski restoring parity for Barca shortly before Ignasi Miquel headed Granada back into the lead with 25 minutes remaining.
However, Yamal had the last laugh 10 minutes from time and ensured that Barcelona came away with a point when he curled a sweet strike from outside the area into the bottom corner.
At the age of just 16 years and 213 days, Yamal has become the youngest player to score a brace in La Liga history, surpassing the previous record held by Ansu Fati (17 years and 94 days) in February 2020.
Yamal has also scored the most La Liga goals (three) before turning 17 years of age, surpassing Fati (two) once again as well as Athletic Bilbao winger Iker Muniain (two).
In addition, Yamal has recorded five goals and five assists in 33 games across all competitions, becoming the youngest player from both Barcelona and Spain to have at least 10 goal contributions in a single season.
Although Yamal was pleased with his individual performance against Granada, claiming the Man of the Match award, the result against Granada has seen Barcelona slip 10 points behind La Liga leaders Real Madrid, while they also sit five points behind Girona in second.
"It was a missed opportunity for us tonight but we must keep working," Yamal told reporters after the match as quoted by Barca Blaugranes.
"I'm trying to work hard with the trust of my manager. I'm very grateful to him but right now I'm thinking of the draw and the missed opportunity.
"All season we've been conceding too many goals close together, too many goals full stop. We have to improve as it's costing us points.
"I am grateful for the MVP awards but I'm sad about the result and that's what I'm left with at full time."
Discussing Barca's title hopes, Yamal added: "There are games to go, the teams ahead of us can drop points and we have to be ready to make the most of it if they do."
Yamal will be looking to add to his goal tally when Barcelona travel to the Estadio Municipal de Balaidos to face relegation-threatened Celta Vigo on Saturday.