In an interview with Parade, the actor - who plays Hector Barbossa in the film franchise - credited Cruz's varied career with helping to "raise the bar" on the project and to provide conflict for hero Jack Sparrow (Johnny Depp).
"She is such an amazing actress. You look at Vicky Cristina Barcelona and that's one of the high comedy acts onscreen. It certainly deserves an Academy Award," he explained. "And you see her in a Pedro Almodovar film as a great dramatic actress. So to have that come in and raise the bar as a principal character, and with Ian McShane, it kept us on our toes.
"It was great for Jack Sparrow to meet his match. It sharpened his wits because I think their dialogue is very sharp and very funny."
Rush recently revealed his plan to take a "nice, hefty break" from showbiz following what he describes as a "pretty heady" few years in his acting career.
He can next be seen in The Green Lantern, voicing the character of Corps member Tomar-Re, a role he confessed that he 'couldn't resist'.
Watch our recent interview with Geoffrey Rush below: