Lead Grammy nominee Kendrick Lamar received a standing ovation as he collected the best rap album award for To Pimp A Butterfly from fellow Compton rapper Ice Cube.
Lamar, who tops the nominations list with 11 nods, has already scored four awards in the pre-broadcast ceremony, including one award for his collaboration with Taylor Swift on Bad Blood.
Collecting his gramophone trophy from Ice Cube and his son O'Shea Jackson Jr, Lamar said: "This is for hip hop, Ice Cube, this is for Snoop Dogg, this is for Nas, we will live forever, believe that."
Swift opened the 58th Grammy Awards with the first TV performance of Out Of The Woods from her record 1989, which has already won an award for best pop vocal album.
The singer showed off her new blonde bob while wearing with a skintight black beaded body suit with sheer panels down the sides.
She was joined on stage by her collaborator Jack Antonoff, from the bands fun and Bleachers, who is the partner of her close friend Lena Dunham.
Swift, who scored seven nominations, has already won two gramophone awards in the pre-broadcast ceremony, including best music video for Bad Blood, her collaboration with Lamar.