She also became the first solo female to win Rap Album of the Year for her debut project, "Invasion of Privacy".
The footage showed his wife Cardi B surrounded by family as she screams and pushes during the delivery of their daughter. Cardi detailed Miller's family wanted her to win if it was not awarded to him.
But, the debate continues with no signs of ending.
She said: "I want to thank my daughter. I remember previous year when I didn't win for "Bodak Yellow" and everyone was like 'Cardi got snubbed.' Now it's a motherf***kin problem?!", Cardi continued. "Rest in peace!" She went on to shout out her choreographer and glam team, and yell "Bronx in the building!" at the top of her lungs.
Posting videos that saw her wax poetic on everything from cheating lovers to the qualities of the pancake chain restaurant IHOP, Cardi snagged a spot on the reality series "Love & Hip Hop", further amplifying her image.
"Every award to me is special", she said.
Lady Gaga and Bradley Cooper have won the Grammy Award for best pop duo/group performance for the song "Shallow" from "A Star Is Born". The little one had already mastered calling Offset "papa" so hearing her name was a huge moment for her 7-month-old baby.
Earlier in the evening, Cardi wowed the crowd with a performance of "Money" on a lavish, cushioned, lounge club set.
The rapper is also unabashed when it comes to politics, recently unleashing a vulgar rant slamming Donald Trump for the U.S. government shutdown.
For her part, Cardi B announced backstage that she would be "sharing" her trophy with Miller.