The hip-hop star also lands a spot at number two as a guest on Ariana Grande's Problem, making her the first artist since the Fab Four in 1964 to land the top two places on the chart with her first two Hot 100 hits.
The Beatles managed the feat with I Want to Hold Your Hand and She Loves You over 50 years ago, following their breakthrough appearance on The Ed Sullivan Show.
Azalea also becomes only the 15th act to score a one-two punch at the top of the countdown in the same week, and just the third woman behind Mariah Carey in 2005 and Ashanti in 2002. She also becomes only the fourth solo female rapper ever to top the Hot 100 - Lauryn Hill, Lil' Kim and Ludacris' sidekick Shawnna previously landed at number one.
It's a great early birthday gift for Azalea, who turns 24 on 7 June (14).
Her Fancy ends John Legend's reign at the top of the Hot 100 with All of Me. The ballad slips two spots to three on the new chart, while Pharrell Williams' Happy and DJ Snake and Lil Jon's Turn Down for What round out the top five.
Meanwhile, Coldplay have stormed to the top of the U.S. album charts with the biggest first-week sales of 2014.
Their new release, Ghost Stories, sold 383,000 copies to become the band's fourth Billboard 200 number one. It's also the first release to top 300,000 sales in a week this year.
Country star Brantley Gilbert's Just As I Am debuts at two with impressive first-week sales of 211,000, and Michael Jackson's posthumous release Xscape slides a spot to three.
Former number ones the Frozen soundtrack and the Black Keys' Turn Blue round out the new top five.
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