Kesha served up some champagne during her NYC show Thursday -- but it wasn't what one paparazzi ordered ... the flying bottle whacked him in the stomach!

Here's how it went down ... the singer was performing at YSL Beauty Candy Club in SoHo last night when she launched into her hit "Joyride," with a couple male dancers onstage as a large crowd of influencers watched.

Check out video, obtained by TMZ ... Kesha is holding a bottle of champagne while belting out the tune with the dancers on their knees around her. She starts shaking the open bottle, shooting bubbly everywhere, spraying her dancers and herself.

Then Kesha provides her own version of bottle service to a photog who's shooting her gig. Kesha tosses the bottle to the side of the stage -- hitting the shutterbug squarely in his torso, splashing him with champagne too.

Kesha clearly didn't mean to strike him with the bottle -- and she even let him know with a hand wave while cranking out the rest of the song. The photog was a good sport about it, giving Kesha a little wave back.

We're told Kesha performed about 4 songs -- and everyone loved it. All's well that ends well!