The 21-year-old star added new verse to his song Black as he hit out at prejudice, and said: "Equality's a right it doesn't deserve credit."
The artist also hit out at prime minister Boris Johnson during the performance.
The Standard has contacted Downing Street for comment.
As he continued his unexpected segment, Dave commented on the treatment of Meghan, and said: "If you don't wanna get it then you're never get it out how the news treats Kate versus how they treat Meghan."
Elsewhere in his performance he paid homage to those killed in the recent London Bridge attack, focusing on Jack Merritt who was killed during the violence, spoke of Grenfell victims and the Windrush generation.
He previously spoke of how he had met Mr Merritt, who was killed during the atrocity at London Bridge last year.
After the attack, Dave tweeted: "Rest in peace brother. One of the most painful things. Jack Merritt was the best guy. Dedicated his life to helping others, was genuinely an honour to have met someone like you and everything you’ve done for us I’ll never ever forget."
Dave ended with a call for "reparations for the times my people spent on plantations".
It was not the first slight at a politician from the night.
After winning the international male solo artist award, Tyler, The Creator made fun of former prime minister Theresa May.
Commenting that she had previously stopped him entering the country, he thanked her in his acceptance speech.