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Tom Hanks Fuming After Fan Trips Wife ... 'Back the F*** Off!!!'

Tom Hanks was seeing red when his wife Rita Wilson was almost knocked to the ground by a pack of his fans ... and the guy who's normally Mr. Cool let 'em know he was pissed off!

Tom and Rita were heading to their car Wednesday night in NYC when the swarm of fans scrambled around for autographs and selfies -- the crowd got so big, one fan bumped into Rita and made her trip.

TH was having none of it -- he rushed to her rescue, then put his hand on one guy and yelled to the rest, "This is my wife, back the f*** off!!"

He gave them quite the death stare for a few seconds before storming off to their car. In the wake of Tom losing it, the finger-pointing started among the fans ... with one guy claiming someone else pushed him into Rita.

Hey, they didn't get pics or an autograph, but the "Elvis" star definitely gave them a night they won't soon forget.

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