Prince Harry -- Spittin' Game to HOT WAITRESS at Vegas Nightclub [Video]

Prince Harry was full on FLIRTING with a super hot waitress at a Las Vegas nightclub Sunday night ... and TMZ has the footage to prove it.

No word on the identity of the scorchin' brunette -- but sources inside XS nightclub at the Wynn Hotel tell us she was VERY LUCKY to get that close to the Prince, because dude was rollin' with an ARMY of security.

What happens in Vegas ... could get this chick into Buckingham Palace if she handles it right.