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Hugh Jackman and Kate Hudson linked up and let loose Monday night, grabbing mics at an NYC pub and belting out a victory duet after snagging a Gotham Award ... in tribute to the singer they covered for the win.

Check out the clip from Old Mates Pub -- Hugh and Kate belting "Sweet Caroline" like karaoke pros, leading the tipsy crowd in a singalong … fresh off accepting the 2025 Gotham Awards’ first-ever Musical Tribute for their flick "Song Sung Blue."

The song choice was spot-on -- it’s Neil Diamond, after all ... the very man at the center of "Song Sung Blue," the film that scored them the award. Getty

Clearly, Hugh and Kate were born for this movie ... proof’s in the footage, as they huddled up with pals, belting their hearts out and wrapping the

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