Injury time win sets up Saturday's decider.
Liverpool manager Jurgen Klopp remains hopeful Virgil van Dijk can play in Saturday's Club World Cup final.
The Dutch defender missed yesterday's 2-1 semi-final win over Monterrey through illness.
Liverpool needed an injury time goal from Roberto Firmino to set up a final meeting with Brazilian side Flamengo.
Naby Keita's early goal set Liverpool on their way but the Mexican side levelled the game just two minutes later.