In a devastating attacking display by Liverpool on the south coast, the Egypt winger was an inevitable scorer to move his league-high tally to 14 goals.
Despite that, Liverpool made a bright start and nearly took the lead after 11 minutes when Coutinho's curling free-kick came back off the upright.
Liverpool are on 31 points, sandwiched between fourth-placed Tottenham Hotspur and sixth-placed Burnley with all three teams 18 points behind leaders City after 17 league games.
"It's not fair to ask those kind of questions, I don't think, but he gives us his all every game and that's all you can ask of him".
Adrian Peterson heads to IR, wants to play next season
It's also possible Peterson's incredible, Hall of Fame career will quietly end after a final season wearing two foreign uniforms. He topped the century mark again November 5 when he torched the San Francisco 49ers for a season-high 159 yards on the ground.
"The front four have been on fire ..." "The start was serious, we knew how they can play if you let them".
"The intensity in the first half maybe we didn't have in the second half".
Coutinho's goal was the highlight. It also erased memories of this fixture last season when Liverpool famously surrendered a 3-1 lead with 15 minutes to go to lose 4-3.
Oxlade-Chamberlain did the same for Liverpool in the second half before Coutinho curled in an enticing cross that Firmino, potentially from an offside position, ran onto and flicked a header past stranded goalkeeper Asmir Begovic.
"I am really pleased about everything", Klopp gushed in his post-match interview.
"He's been the most professional person I've seen all season; he's been top quality from the start and every time he gives his all for the club".