While Magic!'s Rude scored a sixth week at number one, Grande and Azalea enjoy a run of hits including top 10 debuts for Break Free and Black Widow, the Australian rapper's Rita Ora-flavoured tune.
Meghan Trainor's All About That Bass climbs to two on the new chart, while Sam Smith's Stay With Me drops to three.
The Grande/Azalea takeover begins at four with the former's Break Free, which climbs into the top five from 18, while Azalea's former number one, Fancy, slides to five.
The girls of summer also land hits at seven (Problem), eight (Black Widow) and 10 (Bang Bang).
Only 12 acts, including Grande and Azalea, have claimed at least three top 10 spots on the Hot 100 in the same week, but this week marks the first time in the Hot 100's 56-year history that two acts have tripled up in the top 10 simultaneously.