The 18-year-old had been out of action since last November, having suffered a torn meniscus on his left knee in a clash with Real Betis.
The Spain international came off the bench to replace striker Luuk de Jong with less than 10 minutes left of the game and went on to score in stoppage time.
Eric Garcia’s pass made its way towards Fati through a dummy from Memphis Depay.
As the Levante defence failed to deal with the danger, the Barca youth academy graduate took possession in the middle of the visitors’ half and charged towards goal.
Despite full-back Jorge Miramon’s attempt to block his path, he created space with a quick change of direction and sent it bouncing beyond goalkeeper Aitor from outside the box.
The strike saw his side go 3-0 up at Camp Nou, with Depay and De Jong scoring in the first half.
The winger admitted his first game back for the Catalan side went better than he expected and said he is proud to wear the No. 10 jersey that was previously worn by Lionel Messi.
He told Movistar: “I did not imagine a return like this. Here you always have to win. I am happy for the victory; we have a lot left. I thank the doctors and physios who have been with me. Also to the fans.
“I have thought about helping the team. I have also thought about my family, who have suffered these months. Also for the people of the club. They have been a great support for me in all these months.
“I am one more. I will try to add what I can. I will try to help the coach and be available to help.
“It will depend on how I find myself. I will have to earn the minutes. This is very long, it has just begun. We are Barca and we have to fight for everything.
“For me the No. 10 is not a source of pressure, it is a source of pride. I thank the club and the captains for giving me the opportunity to wear it. It is not pressure, but gratitude.
“We are going to fight for La Liga, for the Champions League and for everything. We have to fight and work for that.”