Bradley Cooper Plays with Pearl Jam, Hangs with Gigi Hadid at BottleRock

Bradley Cooper's proving the star wasn't just born, but alive and kicking ... 'cause he hopped onstage to perform a hit song from his 2018 movie -- alongside a rock legend.

The actor put on his singing cap Friday night at BottleRock musical festival in Napa Valley ... performing the song "Maybe It's Time" from "A Star Is Born" with Pearl Jam's Eddie Vedder.

Check out the clip ... it's a pretty intimate moment for such a massive concert experience -- with Eddie and Brad sitting in chairs while Vedder shreds on an acoustic guitar.

If you don't know ... BC and EV have been friends for years -- and, Vedder actually partly inspired Cooper's 'Star Is Born' character. Bradley revealed in an interview during the movie's press tour he spent multiple days with Vedder and asked him a ton of questions to hone his character.

BTW ... Cooper also hopped onstage at the end of the set to sing Neil Young's "Rockin' in the Free World" -- two Bradley songs for the price of one!

It wasn't all work and no play for Bradley though ... 'cause he spent some quality time with his lady love Gigi Hadid -- laughing and dancing while Stevie Nicks performed.

It looks like Gigi tried to keep a low profile in the hat and glasses -- but, Bradley's pretty out there, not covering up whatsoever. No point in going incognito when you're jamming with the band later on anyway, we suppose.

BottleRock's bringing out the A-List's best and brightest FWIW ... Cameron Diaz and Tommy Lee are both reportedly coming out for the weekend -- and, Bradley even got to share the stage with Golden State Warriors star Steph Curry. Talk about star-studded.

BottleRock's final day kicks off Sunday, and acts like Ed Sheeran, Queens of the Stone Age, Dominic Fike, The Offspring, Norah Jones and Stephen Marley are ready to hit the stage.