The Portugal youth international is considered one of European football's brightest talents and he delivered on that reputation with a stunning display that overshadowed Luka Jovic's return to Estadio da Luz.
Serbia striker Jovic, who is in the second term of a two-season loan at Frankfurt from Benfica, got on the scoresheet against his parent club by cancelling out Felix's spot-kick opener, which came after Evan N'Dicka's dismissal for bundling over Gedson Fernandes in the box.
But the shimmering homegrown talent netted twice more either side of a Ruben Dias header to become the youngest player to hit a Europa League treble, although Goncalo Paciencia did later give the visitors a handy second away goal to take back to Frankfurt.
Felix first illustrated his sought-after ability in the 20th minute.
The rumoured Manchester United target sent Fernandes scampering into the box with a cute reverse pass and then, following N'Dicka's panicked push from behind, coolly converted the resultant penalty.
Jovic - tipped to sign for Adi Hutter's men on a permanent basis at season's end - responded 20 minutes later, Ante Rebic breaking into the box and selflessly squaring for him, but parity lasted less than three minutes.
Felix this time took it entirely upon himself to brilliantly fire into the bottom-left corner from 25 yards.
Frankfurt looked to have equalised again when Filip Kostic's tame shot squirmed through Odisseas Vlachodimos, only for the offside flag to go up against two players deemed to have occupied an active position.
Instead, it shipped two more in four second-half minutes.
Dias nodded in Benfica's third after Felix helped on a corner, before the teenager completed his treble by side-footing through Kevin Trapp's legs from Alex Grimaldo's cut-back.
That burst appeared to have dashed the Bundesliga's side hopes of advancing, but Paciencia headed in fellow substitute Jonathan de Guzman's corner 18 minutes from the end to inspire hope of a second-leg fightback in seven days' time.