Rapper Coolio Beats Baby Mama: "He Brought Home A Chick And Beat Me".

Coolio should know better than to bring another woman home to the house he shares with his girlfriend ... and he should also know better than to allegedly punch her in the face.

TMZ has learned the rap legend -- aka Artis Ivey Jr. -- was popped on April Fools' Day after he allegedly pushed Anabella Chatman to the ground and punched her in the face.  And to add insult to injury ... according to the police report, Coolio then hightailed it out of there with their toddler son and the other woman.

Actually ... he didn't get out clean.  Anabella says Coolio struck her with his car as he beat his hasty retreat -- in fact, cops say she had tire marks on her leg.  Pretty compelling evidence.

Coolio tried convincing cops HE was the victim and that she scratched him in a jealous rage, but they weren't buyin' what he was sellin' ... so he was taken to the pokey.

Arrrgggggggggggg..... I hate domestic Violence.
#saynotodomesticviolence