IMPROMPTU DANCE PARTY!!!

Tony Hawk ran into Paul McCartney Tuesday night at the Hollywood bash for his daughter Stella McCartney's clothing line ... and shared the hilarious play-by-play of their encounter.

"Hi Paul, I'm Tony Hawk. You signed a skateboard for our skatepark foundation and I wanted to say thank you."

"Him: 'You're welcome, let's skate!'"

"... Then this happened. So tonight I either danced awkwardly with Paul McCartney or we did sick stationary slalom moves."

Looked like a little bit of both ... with the legends groovin' to a live Grimes set.

TMZ Sports spoke with Tony the day after the event ... and he admitted to being a little starstruck by Sir Paul and another big-time celeb.