The Bajan star's hook-up with Calvin Harris, 'We Found Love', beat off competition from Florence + the Machine, who sit at two with 'Shake It Out'.
Professor Green slips a place to three with 'Read All About It' and Christina Perri's 'Jar Of Hearts' stays firm at four.
LMFAO's 'Sexy And I Know It' completes the top five, while Lana Del Rey's 'Video Games' trails at seven.
Bruno Mars's Twilight track 'It Will Rain' debuts at 11, and JLS's new cut 'Take A Chance On Me' enters at 13.
Labrinth's 'Earthquake' gains a few places shuffling up to 19, while Christina Perri's Twilight track 'A Thousand Years' lands at 27.
Pixie Lott's new single 'What Do You Take Me For?' sits at number 30 and Maverick Sabre's 'I Need' is a few behind at 32.
This week's Irish Top 10 is as follows:
1. (1) Rihanna feat. Calvin Harris: 'We Found Love'
2. (9) Florence + the Machine: 'Shake It Out'
3. (2) Professor Green feat. Emeli Sande: 'Read All About It'
4. (4) Christina Perri: 'Jar Of Hearts'
5. (6) LMFAO: 'Sexy And I Know It'
6. (3) Avicii: 'Levels'
7. (10) Lana Del Rey: 'Video Games'
8. (5) Cher Lloyd feat. Mike Posner: 'With Ur Love'
9. (20) Ed Sheeran: 'Lego House'
10. (16) David Guetta feat. Usher: 'Without You'
Watch the music video for Rihanna's 'We Found Love' below: