Justin and Jaden's Dance Battle at Lucky Strike.

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