Rap sensation Iggy Azalea, enigmatic songstress Sia Furler and country star Keith Urban held 10 nominations between them.
Smith had bested both Sia's "Chandelier" and Iggy Azalea's "Fancy" for Record of the Year. He also defeated Sia's "Chandelier" for Song of the Year.
Pharrell Williams took out two of Sia's categories: Best Music Video and Best Pop Solo Performance for his song "Happy.
Azalea's "Fancy" was also in the Best Pop Duo/Group category with Charli XCX. But it lost out to A Great Big World with Christina Aguilera for "Say Something".
Urban, a winner of four Grammys in previous years, bowed out in two categories - for Best Country Solo Performance for Cop Car and Best Country Duo/Group Performance for Raise 'Em Up with Eric Church.
Beck's "Morning Phase" won Album of the Year and Best Rock Album.
President Barack Obama, pop star Katy Perry and a survivor also appeared via a pre-recorded video stating that nearly one in five women in America has been a victim of rape or attempted rape and one in four women has experienced domestic violence.
"It's not OK and it has to stop," Obama said.
"Artists have a unique power to change minds and attitudes and getting us talking and thinking about what matters."
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