The ceremony went down Saturday night in Cleveland at Rocket Mortgage Fieldhouse -- and Cher's iconic hit, "Believe" kicked things off, as she performed it with Dua Lipa.

When it came time to induct Cher, Zendaya did the honors while rocking a barely-there gown that looked like she borrowed it directly from Cher's closet.

In her acceptance speech, Cher boasted she changed the sound of music -- referring to her early use of auto-tune on tracks like "Believe" -- and called out Cinderella (yes, really) and her mother as inspirations.

She said, “The one thing I got from my mom is to never give up, I'm talking to the women ... down and out, we keep going.”

Julia Roberts was there to Stan for the Dave Matthews Band ... during her induction speech, she said the legendary jam band's appeal was all about "spontaneous abandon" -- which was on full display when DMB hit the stage and got the whole crowd singing along.

Other highlights included Dr. Dre inducting Mary J., noting she helped create a whole new genre of music -- hip-hop soul ... while Chuck D and the Roots paid tribute to new inductees Kool & the Gang, and Keith Urban and Roger Daltry showed up to salute inductee Peter Frampton.

There were tons of other all-star collabs to honor Ozzy, Foreigner, A Tribe Called Quest and Dionne Warwick -- all of whom entered the Hall this year.

Plus, there were posthumous tributes for Jimmy Buffett, Kris Kristofferson, Cissy Houston, John Mayall and Big Mama Thornton.

While One Direction is not in the Hall of Fame, there was a moment of silence during the ceremony to honor Liam Payne ... following the singer's tragic death last week in Buenos Aires.

BTW ... this was Ozzy's second induction to the HOF, as he got in back in 2006 with his former band Black Sabbath. Jelly Roll and Billy Idol teamed up for a musical tribute to rock's Prince of Darkness.