Photo by Cass Bird

After an unexpected sales battle with pop's heir apparent Lady Gaga, it's Katy Perry who proved victorious this week, but her new "Roar" was still unable to overtake Robin Thicke's seemingly unstoppable "Blurred Lines," which remains No. 1 on Billboard's Hot 100 for an 11th consecutive week.

"Roar," originally expected to sell around 400,000 copies, surpassed expectations and debuted with first-week sales of 557,000, according to Billboard. "Lines," which features Pharrell and T.I., recently became Variance readers' Song of Summer.

As we previously reported, "Roar" gives Perry her best sales week for a track, topping her record of 509,000 with 2010's "Firework." It also gives "Roar," which is No. 1 on the Digital Songs, the biggest sales week for a song in 2013.

According to iTunes, "Roar" sold 544,000 copies just on its platform alone. By comparison, Gaga's self-praising "Applause" netted 218,000 copies sold across all platforms and debuts this week at No. 6 on the Hot 100.

"Roar" is the lead single off Perry's new album, PRISM, which is set to arrive on Oct. 22. via Capitol Records.