The 19-year-old delivered a memorable display in Lisbon, with the Portuguese club taking a commanding advantage into the second leg of their quarter-final clash.
The Manchester United target became the youngest player in the competition to net a treble, which will only intensify interest in him from some of Europe’s top clubs, while Ruben Dias also scored for the hosts.
The visitors had defender Enda N’Dicka sent off by English referee Anthony Taylor for a foul after 21 minutes.
Luka Jovic had equalised Felix’s opener, and Frankfurt did not fall completely away, with substitute Goncalo Paciencia’s late goal giving them a glimmer of hope.
Benfica boss Bruno Lage left out top scorer and former Frankfurt striker Haris Seferovic, who had to be content with a place among the substitutes, while captain Andre Almeida was rested and replaced by Sebastien Corchia.
A groin strain sidelined Frankfurt striker Sebastien Haller, but defender N’Dicka and midfielder Sebastian Rode were recalled.
Referee Taylor was soon called into action, booking Jovic, who is on loan from Benfica, for a foul on Rafa Silva after just four minutes.
Frankfurt dominated the early stages, effortlessly keeping possession, but it all unravelled after 21 minutes as N’Dicka conceded a penalty and was red-carded.
He could have no complaints at Taylor’s decision following his challenge on last man Gedson Fernandes, and Felix stepped up to beat Frankfurt goalkeeper Kevin Trapp and put Benfica ahead.
Ante Rebic then followed Jovic by picking up a booking, and Frankfurt knew they had to regroup quickly following the penalty setback and seeing N’Dicka sent off.