The striker, who made the key moves in the semifinal against Mexico's Monterrey with a goal in stoppage time, played a tough, intense final at the Khalifa International Stadium in Doha, capital of Qatar on Saturday.
The 90 minutes went by without a score, but the team coached by Germany's Jurgen Klopp finally downed the Copa Libertadores champion at minute 99, reports Efe news.
Liverpool, six-time European champ, broke a streak of three lost finals (1981, 1984 and 2005) to succeed Real Madrid as the Club World Cup champion and thus kept the dominance of European football going.
Flamengo, champion of the Brazilian league, dominated the first half, suffered in the second and reached overtime with more heart than energy.
Liverpool started the final at full speed. In a scant five minutes it had three chances to score by Firmino (going head-on against Diego Alves), Keita and Alexander-Arnold. No such luck, though the English side made clear why it was the favourite, while the Brazil withstood as best they could the three-pronged Red offensive.
Liverpool's impetus slacked off after the first 15 minutes, however, and ball control went to the Libertadores champion, whose threats began with the tireless work of Gerson at midfield and the devilish speed of Bruno Henrique on the attack.
But the going got heavy and the monotony before halftime was only relieved by a squabble between Mane and Rafinha.
The second half began with the two squads fighting for a goal that could prove to be the winner.
Firmino again failed inexplicably with a medium-high finishing shot that seemed to have no reason not to score until it banged off a pole. Nor did Salah succeed after taking a promising cross into the centre of the area.
And, so it went on until the match came down to extra time, when Mane started a counterattack by racing toward the Flamengo goal and passing the ball to Firmino.
The striker controlled the pass, feinted and blasted the ball into the net to make the score 1-0 at minute 99.
( With inputs from IANS )