Felix struck his third before Goncalo Paciencia headed in for the visitors.
It finished Benfica 4 Eintracht Frankfurt 2 on Thursday night.
It seems remarkable that Felix only made his senior debut this season.
"If he hadn't scored tonight, everyone would have said he is off-form, but because he scored three, they say he is flying", said Lage. He has to go out and enjoy himself and that is what he has done.
Despite being an attacker capable of using both feet no problem, he feels much more comfortable on his right, with which he has managed to score 15 goals, compared to the eight he has netted with his left foot. "He has to develop naturally".
Scouts across Europe were in attendance to watch Felix play for Benfica in their first leg Europa League quarter final game against Bundesliga side Eintracht Frankfurt.
Joao Felix threaded a ball through the Eintracht defence to send Gedson Fernandes clear and he was pushed over from behind by Evan N'Dicka.
Felix scored a hat-trick and supplied the assist for the other goal as he provided further evidence of the talent that has had elite clubs beating a path to Benfica's door this season.
However, the player's father, Milan, has said he wishes to stay put with Frankfurt and fire them into the Champions League. "It's not a great feeling for a keeper because you're the one that has the responsibility to come to your team's rescue".
But Benfica coach Bruno Lage urged people not to get carried away and said: "We need to be calm, let him grow and enjoy it".