On a feisty night under the Anfield lights, the world's most expensive defender proved he can be effective at both ends of the pitch by nodding in an 84th-minute corner to make it 2-1.
Still, very few Liverpool fans seemed too concerned with his price tag in the moments following his victor.
Nearly as recompense for the penalty decision in the league not too long ago in this fixture, referee Bobby Madley blew up as Mason Holgate somewhat tentatively glanced Adam Lallana. A clearly unhappy Firmino vaulted back onto the field and sprinted toward Holgate, swearing in Portuguese, and was lucky that referee Bobby Madley stepped in between them to intervene.
However, he repaid them in fine style to spark wild celebrations at his new home.
In a typically high-octane derby, Wayne Rooney picked up an early booking for a crude tackle on Joe Gomez and was substituted in the 52nd for his own good, moments after escaping a second yellow card for shoving Emre Can. The Blues, feeling scorned, watched as James Milner tucked home the first goal of the match from the spot.
Virgil van Dijk hasn't scored in his debut.
Just like a month ago, Liverpool were made to pay for missing chances as an improving Everton launched a counter-attack from a corner which ended with Phil Jagielka teeing up Sigurdsson to place a shot past a static Loris Karius.
It was a questionable call, but the visitors shrugged it off to fight back and equalise through Gylfi Sigurdsson, only for £75million Reds debutant Virgil van Dijk to win it for Jurgen Klopp's side.