Roberto Firmino's 99-minute strike saw the Reds triumphed over their Brazilian counterpart in Doha
The Reds had initially controlled the game earlier in the first half, with Firmino hooking a great chance over the bar inside a minute before Naby Keita shot wastefully over inside the box and Trent Alexander-Arnold drove narrowly wide from distance.
However, Copa Libertadores champions Flamengo came back strongly, with winger Bruno Henrique beating Alexander-Arnold on a couple of occasions and forcing a superb covering block from Joe Gomez on 26 minutes.
Mo Salah then squandered a great counter-attack opportunity as red shirts flooded forward from a Flamengo corner before Keita was denied a free-kick on the edge of the box when he was blocked off by former Chelsea defender Felipe Luis.
In the second half, Firmino had another glorious chance to break the deadlock. He flicked the ball over his marker in the penalty area but his shot into the ground came back out off the inside of the post with goalkeeper Diego Alves stranded.
Once again Flamengo were able to stem the tide before there were major concerns for Alex Oxlade-Chamberlain when he landed awkwardly on 72 minutes with what looked like an ankle injury and was replaced by Adam Lallana.
VAR drama then took centre stage in injury-time, when Sadio Mane appeared to have been brought down in the penalty area by Rafinha after bursting through on goal from an inch-timed pass from Firmino.
Liverpool had lost in the 1981 final of this competition to Flamengo and finished runners-up in 1984 and 2005, but deep into a tense and draining night in Doha, Firmino kept his cool magnificently to cap a brilliant breakaway and fire in the winner on 99 minutes, sparking wild celebrations from Liverpool's players.
Jurgen Klopp's side eventually saw off their talented, spirited opposition on Saturday night to make it three major successes in three finals, in a single year (2019) for the Merseyside Club.