The singer's edgier-than-usual look featured a high-leg design with cutouts resembling garters just below her hips. The curve-hugging one-piece was embellished with lacing down its center ... parting at the chest to tease her cleavage.

Fans drooled over the risqué outfit ... with tons online calling her "mother" and applauding the more grown-up look.

Olivia sang her big hits at Lollapalooza ... including "Vampire" and "Drivers License."

She also belted her playful punk-pop single "Bad Idea, Right?" ... furthering herself from her Disney Channel roots by shaking what her momma gave her to the beat with her back turned to the crowd.

Liv momentarily strayed from her discography and covered No Doubt's "Don't Speak." Remember ... she joined the band on stage at Coachella last year to perform their 2000 song "Bathwater."

The "Guts" artist's fan-approved performance makes her announcement as one of Chicago's Lollapalooza main acts that much more exciting.