13yearoldxfactor.jpgX Factor/Fox

The X Factor premiere kicked off last night with Rachel Crow ... a 13-year-old singer who belted out Duffy's hit "Mercy" (click through to watch the clip).

After her powerful performance, judge Paula Abdul said, "You opened up your mouth to sing and blew us away."

Simon Cowell added, "We're going to hear a lot about you."

The teen is hoping to win the show's $5 million prize ... to help her family buy a new house. Crow told the judges, "We live in a two-bedroom house, and I have six people in my family. I'm a girl. I need my own bathroom."

Sassy!

Meanwhile, a slightly less-talented contestant surprised Paula with HIS X Factor, almost exposing himself on stage and causing Ms. Abdul to walk off ...