Before that, she'd only really been seen in a handful of online videos, but by the time of the song's official release in February last year – it went straight to No 1 and ended up selling more than 480,000 copies – she was one of the most talked-about singers in the country.
As an introduction, it clearly worked, and Ora's subsequent two singles, RIP, with Tinie Tempah, and How We Do followed Hot Right Now to No 1.
Meanwhile, her debut album, Ora, topped the chart, finishing the year with sales of around 240,000.
"That's the most surreal thing that's happened to me," says the 22-year-old Kosovan-born star.
"The success of the singles, and the tour selling out within minutes of the tickets going on sale– all of last year was crazy."
Ora is getting used to "surreal". She was signed by Jay-Z's management company and record label Roc Nation in New York after Mr Beyonce himself called to request a meeting.
At the time she was at college studying for her A-levels and working in a London shoe shop in order to pay musicians to play with her at gigs in the evenings.
"I'd play anywhere – bars and clubs, in my dad's pub, just to be out singing," she says. "I guess Roc Nation heard about me just through people they know in the industry, called me up and asked for a meeting.
"It was a real pinch-yourself moment, and the meeting we had when I met Jay-Z was just unbelievable. It was so nerve-racking, interesting, exciting and weird all at the same time. You know when you can feel someone's power? It was like that, you could just tell when you walked in the room that he was powerful and successful.
"It was so odd. I walked in, shook his hand and then we were suddenly having a conversation.
"Now it feels like we've known each other a long time. I get lots of advice from him. He's not just a great friend, but a boss and a brother. He's the man."
That is a rather simplified version of events, of course. Multi-million-selling artists and business moguls like Jay-Z don't just call 18-year-old singers in London on the off chance. Ora has pursued a career in showbiz from a young age and went to the prestigious Sylvia Young Theatre School in London.
"I really didn't think I'd be good enough, but then the only thing I was ever interested in was singing. Ever since I was really little, like six or something, it's all I've wanted to do."
The transition from theatre school to a professional life as a performer was difficult, she admits, and there were a few bumps along the way.
"There are so many people leaving there each year as brilliant performers, plus all the other schools putting out the same amount of quality.
"I didn't want to go to another performing arts college after I'd done my GCSEs. I just went to a regular college and carried on writing my songs. I followed my gut, really.
"The first time I thought I might make it was when I was 14, when I was signed to a production company. That didn't work out. A year later, I was signed to a management company, but that didn't work out either.
"There were a lot of promises, but nothing came of them. The important thing is you believe it's going to happen eventually, and that keeps you going."
Ora was born in Pristina in the former Yugoslavia, now Kosovo, and moved to the UK with her Kosovar-Albanian parents when she was aged one, during the brutal conflict in the region.
She says the people of Kosovo have been hugely supportive of her, and she's "so proud" of her birth nation.
Family clearly matters. She took them to Dubai for Christmas and New Year, and when she had a well-publicised wardrobe malfunction on stage which left one of her breasts exposed, the first and only person she had to call was her mother, to apologise and promise it would never happen again.
Immediately after her UK tour, which Ora's currently rehearsing for, she has dates in Australia, and then mainland Europe. Between now and the summer she'll record her second album, and hopes to have it released by the end of the year.
"My first album was finished when I was 19, and I'm 22 now, so I have a lot more I want to talk about and say," she adds.
Ora's self-titled debut featured production from the likes of Major Lazer, will.i.am, The-Dream, Stargate and Diplo, but she promises the second album will see fewer writers contributing more.
"I'm very excited about some of the people lined up, I can't wait to work with them. But obviously I can't say who they are yet. Pop music's very secretive."
l Rita plays Glasgow's O2 Academy tonight. Sold out.
RITA ORA came from nowhere to release three No 1 singles and a chart-topping debut album. On the eve of her first UK tour, which visits Glasgow tonight, she talks to Andy Welch about her stunning rise to fame