Yamal, who doesn't turn 16 until July, came off the bench for the final 10 minutes to become Barca's youngest ever debutant in the Spanish top flight.
"I told him to try things and he did," Xavi said of Yamal's debut. "At 15 years old, just imagine it... He is special and he could have even scored tonight, but [Betis goalkeeper Rui Silva] saved.
"He played with confidence and he showed what he is about. He has no fear and bags of talent. Some of his passes in the final third were really good."
"He's a similar player because he has that innate talent in the final third which is difficult to find," Xavi added when asked if the three could be compared.
"Lamine doesn't seem like a 15-year-old, he's very mature. He's ready [to play] and he is training well. He can mark an era at this club as part of this team."
Yamal was given a roaring reception from the 88,000 crowd at Spotify Camp Nou and Barca forward Raphinha, who scored the third goal in the win over Betis, said it won't be long until he scores his first goal for the club.
"We were talking about it on the bench and I think when I was 15 I was playing for the local team in my neighbourhood," the Brazil international told reporters.
"Seeing him come on in front of the fans was incredible. It would have been even better if he scored, but I am sure he will get one sooner rather than later."
Robert Lewandowski added the second and Raphinha the third, with an own goal from Guido Rodriguez completing the scoring late on after Xavi had also brought on Ousmane Dembele, who returned from a three-month injury layoff.
The victory restored Barca's 11-point lead at the top of the table over Real Madrid as they close in on a first title since 2019 and saw the team return to winning ways after the shock loss at Rayo Vallecano in midweek.
"After the deserved defeat in Vallecas, we needed to react," Xavi added. "We started well. We were already a goal up when the red card arrived.
"We basically killed the game off in the first half. It was a well-rounded performance from the team, we were able to rotate and give minutes to other players. It's another step towards our objective.
"It was important for Dembele and Christensen to get minutes. Dembele told me he felt good. We have missed them both. They are special players."
The defeat leaves Betis nine points back from the fourth and final Champions League qualifying spot.
Coach Manuel Pellegrini accepted Barca were the better side, but he was not happy about the red card, with Edgar dismissed for fouls on Raphinha and Pedri in the first half after coming on for the injured Luiz Felipe.
"The game lasted 20 minutes," Pellegrini said. "Barcelona dominated, scored from a corner and then the game ended with an absurd dismissal.
"If you ask me, neither of the challenges are bookings. The first one is justifiable because it's [the referee's] criteria, but the second has no explanation because it goes against his criteria.
"The referee himself said two times it's not a yellow and [Barca's players] made him change his decision. He didn't show any character."