Pep Guardiola’s side, taking part in the tournament after winning last season’s Champions League, made the ideal start.
This was as Alvarez struck inside the first minute, chesting in from close range after Nathan Ake’s long-range strike hit the post.
They added a second before the break when Nino turned Phil Foden’s cross into the back of his own net.
England’s Foden then got on the scoresheet himself in the second half when he darted through the middle to prod in Alvarez’s cross before the Argentine forward got his second in the 88th minute with a clinical strike into the far corner.
Success meant City emulated Manchester United, Liverpool, and Chelsea in lifting the Club World Cup, but became the first English side to win five trophies in a calendar year.
The Treble of Premier League, FA Cup and Champions League last season was followed by the Uefa Super Cup in August.
But some of the shine was taken off their victory by the sight of Rodri – so influential for the side – going off injured towards the end of the second half.
Meanwhile, Egyptian side Al Ahly claimed third place with a 4-2 win against Urawa Red Diamonds of Japan.
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