The 22-year-old singer is also re-writing the record books, as her fifth number one makes her the first female solo artist in chart history to achieve five number one singles in consecutive years, according to the Official Charts Company.
What's My Name, which took top spot last night, follows Only Girl (In The World) (2010), Run This Town (2009), Take A Bow (2008) and Umbrella (2007).
The only other solo artist to equal the achievement was Elvis Presley in the 1950s.
What's My Name, which features Drake, climbed from second place to bump X Factor champion Matt Cardle off the summit.
His cover of Biffy Clyro's When We Collide slipped down one place after three weeks at number one.
Rihanna's two other songs in the top 10 are Only Girl (In the World), which slipped from sixth to ninth, and Who's That Chick with David Guetta, which climbed from 13th to tenth.
The Black Eyed Peas hung on to third spot with their track The Time (Dirty Bit), sampling the Dirty Dancing theme.
In the album charts, second and third spots were still held by Plan B and Take That.