Jurgen Klopp's men will now face Flamengo in the competition's showpiece this Saturday.
The European champions took the lead through Naby Keita after 11 minutes, but were quickly pegged back by a Rogelio Funes Mori strike moments later.
Both sides enjoyed a series of chances throughout the rest of the first half and second period, but it was Roberto Firmino who settled the match for Liverpool one minute into injury time.
So how did the two teams fare? See the gallery below for our player ratings.
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