Eight Mile claims Spotify had about 280 billion unpaid music streams from 2011, resulting in unpaid royalties of as much as US$120 million.
The National Party used the song 186 times during the campaign before taking the ad off the air, the court says.
It is the US rapper's ninth straight album release to hit number one.
The eight-month gestation of "Kamikaze" was the quickest in which Eminem has recorded any album.
Eminem, the top-selling rapper of all time, addressed speculation of the relationship as he headlined the Governors Ball festival in New York.
Eminem and Cardi B were among the biggest names to perform at Coachella.
Eminem in his profanity-laden salvo decried Trump as both incompetent and prejudiced, rapping: "Racism's the only thing he's fantastic for."
Eminem uploaded on YouTube the new song, entitled "Campaign Speech," in which he offers his take on America in 2016 in a freestyle rap largely without a musical backdrop.