Jimmy Fallon and Fox News' Greg Gutfeld caught up like a pair of chummy old friends on 'The Tonight Show' Thursday ... giddily recalling their drunken meeting in NYC and completely kicking politics to the trashcan.

Check out the clip ... the right-wing host recalled meeting a sloshed Jimmy in an "illegal speakeasy" in New York City -- where he says Jimmy tackled him with a hug like a "giant golden retriever." The Tonight Show Starring Jimmy Fallon

After Jimmy "wrestled" Greg and his pal ... they decided to head out to another bar -- which Greg deemed was a gay bar because "the bartender at 6 o'clock takes off his shirt." Getty

Jimmy and Greg had a grand 'ole time going down memory lane together ... later moving the conversation onto Greg's game show, "What Did I Miss?", whic

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