Vinicius was involved in three of Madrid's goals as they came from behind to claim a two-goal cushion at the Santiago Bernabeu on Thursday.
The teenager's combination play with striker Karim Benzema impressed as Vinicius took his tally of assists in this season's Copa del Rey to five, with captain Sergio Ramos scoring twice.
Injuries to attackers Marco Asensio and Gareth Bale have provided Vinicius with opportunities to shine and Solari has put his faith in the youngster ahead of Spain playmaker Isco, who was on the bench again.
And after Vinicius starred for Madrid, Solari was full of praise for the 18-year-old, who arrived at the club from Flamengo last year.
"He has had a great growth," Solari told reporters. "He showed things before arriving here, later in Castilla and now he is showing them in the first team with continuity.
"He has a lot to grow. He brings a lot of freshness and daring. He has the support of the mature players of the squad, who are always the basis of any serious sports project.
"He is very young, but has a fantastic and surprising evolution. We have to take care of him and in that we are all there to help him, not only in the games but in daily life, in the dressing room and in training.
"Vinicius and Benzema understand each other very well, they do it naturally and instinctively. Both connect and that is very nice."
Solari was unwilling to give any clues as to his plans for Vinicius when he has a full squad of attackers at his disposal, however.
"Each game is a new battle. We will see what happens," the Madrid coach added.
"The important thing is to have Bale, Asensio and Vinicius hold their level, like Benzema.
"Delivery, effort, heart, order and intensity, that's what it's worth and also that each one raises their level."
Que gran partido en el Bernabéu frente a nuestros aficionados! ¡juntos somos más fuertes! a seguir mejorando! ¡HALAMADRID! pic.twitter.com/caQ6b1UcXJ— Vinicius Jr (@vini11Oficial) January 24, 2019
After Marcos Llorente conceded a penalty for handball, Girona levelled the tie at 2-2 but late goals from Ramos and Benzema put Madrid in control of the quarter-final.
Solari, though, insists Madrid still have work to do if they are to progress to the semi-finals at the expense of Girona, who knocked out Atletico Madrid in the last round.
"It's football, that's why this sport looks good," he continued. "You have to keep working the same way because it was the right path. The tie is open and we will have a nice match on the return."