The hosts took an early lead in the first-half, when Bruno Fernandes’ effort was deflected in via Nat Phillips.
However, Liverpool grew into the game and scored a deserved equaliser through a clever Diogo Jota flick following a corner.
Then just before the half-time whistle, Firmino took centre stage, firing home a header from Trent Alexander-Arnold’s pinpoint centre.
Shortly after the break he scored his second and the Reds’ third when he capitalised on a Dean Henderson error.
It brought his Premier League tally for the season up to eight as he backed up Jurgen Klopp’s glowing assessment from earlier this season.
Firmino, who has been a key part of Klopp’s revolution at Anfield, has faced intense criticism for a lack of form, particularly after Jota’s arrival from Wolves last summer.
Many have suggested he should come out of the side, only for his manager to describe him as the ‘complete footballer’.
“Scoring was always important for Bobby. But Bobby is a complete footballer,” he explained last year.
“A football team is like an orchestra, you have different people for different instruments. And some of them are louder than others, but they are all important for the rhythm.
“Bobby plays like 12 instruments in our orchestra! He’s very important for our rhythm.
“We can play well without him as well, but I certainly want him on the pitch and if you look at the numbers, I like it a lot having him on the pitch. Really awesome.”
And Klopp’s sheer delight at Firmino’s first was clear to see as he clenched his fists and screamed on the sideline.
He has previously admitted that he and the players take extra delight when the 29-year-old gets himself on the scoresheet, due to outside pressure placed upon him.
“I’m not concerned about anything with Bobby, but I know from time to time it happens that he scores a goal!
“Obviously the players read newspapers, unfortunately, and they saw there was some criticism, so they were really happy for him to score.”
Sign up to the Mirror Football email here for the latest news and transfer gossip