Their film was called "Argo", a Star Wars rip-off with a story with Middle Eastern revolutionary themes that might have made it a hit in the Islamic Republic.
But it wasn't just the Revolutionary Guard the operation had to fool. The film also had to look like the genuine article in Hollywood where "people lie for a living".
Which means this is a tale of two cities - ticking-clock jeopardy in Tehran interlaced with a hoot in Hollywood where a makeup artist with CIA connections (Goodman) and a old-school producer (Arkin) help Mendez set up an Argo production office.
The worry in that divide might have been that the movie would fall down a gap between the movie-biz satire and life-or-death drama. It's a risk in a movie involving a large blue Wookie lookalike at a fake Argo press launch in Beverly Hills.
But Affleck, already juggling playing Mendez and directing duties, finds a way to keep all his story plates spinning. It's a film of crackling tension-and-release, the nerves alleviated by the Goodman-Arkin double act and the film's running knock-knock punchline: "Argo **** yourself!".
It does however come with curiously schmaltzy bookends involving the Mendez character which seem clumsily designed to make this smartest guy in the room seem more human.
And, of course, an indignant half a star off for the film suggesting the New Zealand and British Tehran embassies turned the six away.
But if it's just "based" on a true story, it also puts you right there on the angry streets of a city where seemingly everyone wants to kill you but for the maple leaf flag badge newly pinned to your lapel.
It takes liberties but Argo neatly spins the sort of yarn which earns it that high recommendation: you couldn't make this stuff up.
Stars: 4/5
Cast: Ben Affleck, Bryan Cranston, Alan Arkin, John Goodman
Director: Ben Affleck
Rating: M (violence, offensive language)
Running time: 120 mins
Verdict: Affleck plays a terrific spy game
-TimeOut