Gavi scored Spain's fifth goal in a 7-0 thrashing of Costa Rica - La Roja's biggest-ever World Cup victory.
The Barcelona midfielder's World Cup goal, a brilliant volley with the outside of the foot which went in off a post, came at the age of 18 years and 110 days.
Pele scored against Wales in a 1958 quarter-final at the age of 17 years and 249 days.
Enrique said: "Gavi is a unique player. He is 18 but he has the personality of an experienced player.
"He's a boy who needs a little bit of calm sometimes. But we are happy to have him in the team and he's going to be one of the stars of world football."
Gavi became Spain's youngest goalscorer when he scored against the Czech Republic and before his 18th birthday in June.
He is now Spain's youngest scorer at a World Cup.
Ferran Torres, with a brace, Dani Olmo, Marco Asensio, Carlos Soler and Alvaro Morata were also on target as Costa Rica were crushed.
"We don't have one striker who scores many goals," Enrique said. "But we have lots of players who score goals and I have never been worried about the lack of goals.
"We are always the highest scorers in competitions.
"This was a very special game for us and we wanted to start the competition in the best way possible. We don't start well (in tournaments). We almost never win the first game, but we have managed to break that."
Spain play Germany - surprise 2-1 losers to Japan - on Sunday and could effectively put the four-time winners out of the tournament.
Asked about that possibility, Enrique said: "I don't want to speculate on that. Germany is an amazing team.
"We have to be calm, even though we have had a big victory.
"I don't think they had one chance. We dominated from the first minute and we created spaces to have good chances."
Costa Rica, quarter-finalists in 2014, were the last team to qualify for the World Cup after beating New Zealand in an intercontinental play-off in June.
Head coach Luis Fernando Suarez said: "I am feeling very sad. There's no doubt about that. I had very different expectations for this match.
"Spain played an amazing game and we didn't. We have players who are better than today.
"We have to forget about this result and start thinking about the next game, however difficult that may be."