Billie Eilish always has time for her fans ... proving she's really a woman of the people by stopping the SAG Awards to sign an autograph -- directly on Melissa McCarthy's face!

The singer-songwriter and the actress hit the stage to present the award for Outstanding Female Actor in a Comedy Series ... and Melissa -- playing up her trademark comedic enthusiasm -- couldn't help but gush over Billie.

After excitedly rambling on about all the times she'd met BE, Melissa asked her to sign her chrome silver dress ... something Eilish turned down because she said she didn't wanna ruin the gown.

So, McCarthy upped the stakes ... asking if Billie would sign her face, an opportunity Billie hopped on without much delay.

She then went to town with black Sharpie on Melissa's forehead, covering her mouth while putting the final flourishes on her signature.

The two stars are clearly having a ball, 'cause it seems Billie couldn't help but crack up laughing during the bit.

Of course, Billie's at the ceremony 'cause she contributed to the soundtrack for "Barbie" -- which is up for four awards tonight.