Pedri, who only returned from a long-term injury in January, was rested from the start against Valencia, but came on and looked to have scored Barca's fourth from distance at a time when the home side were on top at Mestalla.
The goal was later taken off Pedri and credited to Pierre-Emerick Aubameyang, who in turn recorded a first hat-trick for his new side, but Xavi was still effusive in his praise of the teenager.
"There is no player in the world with as much talent as Pedri -- and he is only 19!" the Barca coach said in his post-game news conference.
"He is absolutely superlative. How he turns, his understanding of space and time and the fact he uses both feet. It is amazing to have him in the team and we must take care of him.
"He came on for half an hour and was important. He makes the difference: in how we play, in the box... he wins balls back. We demanded he shoot more and now he has three goals [since coming back from injury].
"Look, he's not a normal player. There are very few like him. Perhaps, at his age, he is already the best in the world in his position."
Replays showed Pedri's strike shaved Aubameyang's back on its way in and the referee's report awarded the goal to the former Arsenal striker, meaning he completed his treble having opened his account for Barca in the first half with a brace.
"Aubameyang's scored goals throughout his career," Xavi said. "He's good in space. He's mature, intelligent, humble and positive. I am delighted with him. Those goals today will give him a lot of confidence."
Barca midfielder Sergio Busquets added: "Auba's worked well since the day he arrived at the start of February.
"He had not played many minutes before arriving and this was just his second start for us, so I hope he can keep helping in this way. He's a great player, he came for free and it's luxury to have him here with us."
Aubameyang, who signed a deal with Barca until 2025 with a break clause in 2023 after rescinding his contract with Arsenal, was quick to point out after the game that he's always done well when playing in Valencia.
"Mestalla is like a second home for me," he told Barca TV. "The last time I played here, I scored a hat trick in the semifinal of the Europa League for Arsenal; today a brace. This stadium has been good to me. I like playing here!"
Frenkie de Jong was also on target as Barca took a three-goal lead inside 38 minutes, with Carlos Soler scoring Valencia's goal just after the break as they threatened an unlikely comeback before Pedri's strike.
Barca are now unbeaten in nine LaLiga games and have lost just once in the league since Xavi took charge in November. Sunday's win moved them back up to fourth, ahead of Atletico Madrid courtesy of their superior goal difference but with a game in hand.
"I am really happy, above all because we've won a big game which gives us confidence," Aubameyang added. "We had played well in recent games, but we had not got the results. This is a huge win going into the important match against Napoli."