Derek Jeter -- Hangs with Jay Z ... See, I'm Urban!

Derek Jeter proved he IS down with hip-hop Thursday night ... shaking hands and hanging out with the most powerful man in rap ... Jay Z ... as the two kicked it courtside at the Clippers game.

Both Jeter and Jay got their hands on the hottest tickets in town -- and had great seats to watch the Clippers implode to the best team in basketball ... despite a 10 point lead in the 4th quarter.

Sad.