Ryan Coogler and Paul Thomas Anderson dominated the night at the Oscars Sunday night, but any competition between them was clearly friendly ... we got the directors celebrating their success together right after the show.

Watch the video ... as Ryan was leaving the West Hollywood hotspot Craig's, PTA appeared to be entering. You can see them embrace as soon as they spot each other, showing tremendous mutual respect.

As you know ... Coogler won Best Screenplay for "Sinners" ... while PTA won Best Adapted Screenplay and Best Director for "One Battle After Another."

While the two films seemed to be the frontrunners for Best Picture ... the award ultimately went to 'Battle.'

Congrats, fellas!