The 21-year-old fended off competition from New Yorkers fun., whose 'We Are Young' climbed from five to two, just under 1,000 copies behind Ora.
Carly Rae Jepsen's 'Call Me Maybe' was a non-mover at three, while Alex Clare's 'Too Close', which features on the current Internet Explorer advert, also remained at four. Last week's runner-up and former number one, 'Young' by Tulisa, however, dropped three to number five.
Although contenders for the top spot midweek, The Saturdays claimed this week's highest new entry, with '30 Days' arriving at seven. Other debuts include Nigerian singer-songwriter D'banj at nine with 'Oliver Twist' and the return of Scissor Sisters at 12 with 'Only the Horses'.
Professor Green's 'Remedy', featuring Ruth Anne, also made its first appearance in the Top 40 at 27, while grime MC Skepta's 'Make Peace Not War' entered at 29.
After the death of disco queen Donna Summer at the age of 63 on Thursday (May 17), several of her hits have re-entered the top 200, with 'I Feel Love' the highest charting at 45.
Other Summer entries include 'Hot Stuff' at 111, 'This Time I Know It's For Real' at 114, 'Love to Love You Baby' at 138 and 'State of Independence' at 143.
Watch the video for Rita Ora's 'R.I.P.' below:
Source: Official Charts Company
> This week's albums chart