Tony Hawk Bros Down with Paul McCartney

What happens when the king of extreme sports meets one of the Beatles?

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.