The Argentina forward reached the landmark with a 24th-minute header at Chase Stadium in Miami.
He then provided the assist for the second goal, setting up Casemiro in the 81st minute to seal victory for the Major League Soccer side against the Liga MX champions.
The Campeones Cup pits the MLS Cup winners against the winners of Mexico's Campeon de Campeones.
Inter Miami took the lead when Messi rose to head in from a cross to bring up his century of goals for the club.
Cruz Azul pushed for an equaliser after the break but were kept out by the Miami defence.
Messi then created the decisive second goal, playing in Casemiro to finish and secure the trophy.
The victory is Inter Miami's latest piece of silverware since Messi joined the club and levels the overall series between MLS and Liga MX clubs at four wins apiece.

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