Eminem All Business Introducing Barack Obama at Kamala Harris Rally, Obama Raps

Eminem kept it all business opening up for Barack Obama at a Kamala Harris event in Michigan ... but Barack Obama was so loose, he started rapping a famous Em song.

Slim Shady just introduced Obama at Tuesday's Harris campaign rally in Detroit, and he kept it pretty brief and played things straight ... but when Barry O came out, he lost himself in the music.

Ya gotta see the video ... Obama takes the baton from Eminem and start's rapping Em's "Lose Yourself" at the podium ... and the crowd goes crazy.

After Obama paid homage to the Detroit icon by showing off his rap skills, he started taking shots at Donald Trump ... taking a dig at the crowd sizes of Harris' opponent, and bashing DT for selling merch on the campaign trail.

Barack kept flaming Trump ... comparing him to someone's senile grandpa and telling folks it's time to turn the page on Trump for good.

Eminem's used to being the headliner ... but he's content to play opener for Obama here ... and it will be interesting to see if the duo helps deliver Harris a key state in the race for the White House.