Firmino, who scored a dramatic injury-time winner against Monterrey to send Liverpool into the final, produced a composed finish in the 99th minute as the Reds became the second English side to win the tournament, after Manchester United in 2008.
In a dramatic conclusion to normal time, Liverpool had seen an injury-time penalty decision overturned after Sadio Mane went down under a challenge from Rafinha, with referee Abdulrahman Al Jassim reversing his initial verdict after checking the pitchside monitor following a consultation with the video assistant referee.
Brazil forward Firmino squandered the opportunity to put Liverpool ahead inside the opening minute at Khalifa International Stadium, blazing over the bar before Naby Keita and Trent Alexander-Arnold also spurned early chances as the Premier League leaders made a blistering start.
Firmino agonisingly hit the post and Mohamed Salah shot narrowly wide shortly after half-time, but Flamengo responded well to early pressure in both halves and posed Liverpool problems – striker Gabriel Barbosa’s attempted bicycle-kick typifying the Brazilian side’s steadily growing confidence.
Liverpool suffered an injury blow as Alex Oxlade-Chamberlain appeared to fall awkwardly on his ankle, and with the prospect of extra time approaching Jordan Henderson’s powerful, curled strike from the edge of the box was superbly tipped over by Flamengo goalkeeper Diego Alves.
Firmino’s breakthrough in the first half of extra time delivered huge relief for Klopp’s side, and while Salah was denied by Alves soon after, the Premier League side were able to see out the second period unharmed.
Mexican side Monterrey earlier defeated Saudi Arabia’s Al Hilal 4-3 on penalties after a 2-2 draw to claim third place.