MindUP -- Goldie's charity focused on supporting kids' mental health and preventing suicide -- held it's 20th-anniversary gala Saturday night called "Goldie's Love In" where Short and Hudson showed off their pipes for the audience.

After a few jokes about Kate's leggy ensemble, Martin starts up the band ... jumping around like a giddy schoolboy before belting out the opening notes of Frank Sinatra's "The Lady is a Tramp."

After their duet, Martin let Kate take the stage solo -- she recently put out an album, after all -- where she sang a couple original songs ... before finishing off with an ode to Tina Turner. Watch the clip until the end to see it all.

While Goldie ran the whole event beautifully, she also grabbed some alone time with her longtime partner, Kurt Russell ... who slow danced with his better half later on in the evening.

While not married, the two have been together for more than 40 years ... and, the flirty energy between them is still obvious when ya watch the clip.

That doesn't mean it didn't get a little contentious between the two during the auction portion of the evening though ... 'cause KR and GH went after the same item.

The couple bid back and forth on a $100,000 credit with private jet company Bajit, and Goldie ended up taking it for $135,000. Listen to her talk to her accountant during the event ... sounds like she's already thinking about tax season.

Among the other stars in attendance ... Demi Moore, Fergie -- who we're told paid $16k for a Mr. Brainwash original painting -- Macaulay Culkin, Melanie Griffith, Orlando Bloom, Max Greenfield, Rachel Zoe, Oliver Hudson and many more.