The song is the Chandelier hitmaker's first Billboard Hot 100 number one as an artist, and her collaborator Sean Paul's first chart-topper in over a decade.
Ironically, Rihanna had planned to record Cheap Thrills for her Anti album, but Sia hit the studio with the song instead.
The Australian joins Madonna and Cher among the only females over 40 to reach the top of the Hot 100.
Sia turned 40 in December (15).
Drake's One Dance drops to two on the new Hot 100, while Calvin Harris' This Is What You Came For rises to three, and Justin Timberlake's Can't Stop the Feeling! and The Chainsmokers' Don't Let Me Down round out the new top five.