Bieber and Jaden Smith The Epic Dance Battle

9/5/2010 10:00 AM PDT

Justin Bieber and Jaden Smith dance-off

Justin Bieber and Jaden Smith aren't usually rivals -- but TMZ has learned the two young superstars went toe-to-toe a few nights ago ... in the form of a dance-battle at a NY bowling alley.

TMZ has obtained pictures of Biebs, 16, and Smith, 12, in action at the Lucky Strike Lanes & Lounge on Tuesday night ... following their concert at Madison Square Garden.

We're told the dynamic duo got down to Kevin Rudolf's song "You Make the Rain Fall" -- and the whole thing was captured on tape by Bieber's documentary crew.

Our sources say both guys "killed it" on the dance floor ... but we're told Bieber was the clear winner ... when he busted out a moonwalk!