Pep Guardiola's side were playing in the competition for the first time thanks to their Champions League win last season.
City saw off Japanese side Urawa Red Diamonds 3-0 in the semi-finals on Tuesday to set up a final against Brazilian outfit Fluminense.
The Copa Libertadores champions named former Real Madrid star Marcelo in their starting XI.
Despite his experience, the 35-year-old gave the ball away to City, who saw Nathan Ake hit the post before Alvarez scored the rebound.
The Argentinian did so after just 40 seconds, with the treble winners getting off to the best possible start.
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As Erling Haaland couldn't feature in the match due to FIFA rules, Alvarez was named up front for City against Fluminense.
The goal is his ninth of the season across all competitions, with the 23-year-old enjoying a hugely successful past year or so.
He won the World Cup with Argentina last December before lifting the Premier League, Champions League and FA Cup with City.
Last season's treble winners doubled their lead in the 27th minute when Foden's shot took a deflection off Nino and looped in.
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Foden finally got himself onto the scoresheet in the second half, before Alvarez scored his second late on to complete the rout.
The Club World Cup is City's fifth and final trophy for 2023 and follows their Super Cup win earlier in the season.
They could be set to win five honours in total during the the campaign as the Premier League, Champions League and FA Cup are still up for grabs.
City's dominance in football has stretched from England to Europe and now worldwide as they celebrate their 14th major honour under Guardiola.