Burke's recording of the Leonard Cohen classic sold 576,000 copies last week, outselling the rest of the top 20 combined.
Its sales tally makes it the fastest-selling single by a female artist in UK chart history, beating the previous record held by Leona Lewis and 'A Moment Like This'.
"This is absolutely crazy, I can't believe it. It's been the best week of my life," Burke said. "Thank you so much to everyone that has supported me and bought the single. I'm bursting with excitement right now, it's incredible!"
Jeff Buckley's interpretation of 'Hallelujah' - taken from the late singer's 1994 album Grace - sold 81,000 copies to chart in second place, while Leona Lewis sold 72,000 copies of 'Run' to claim third position.
Meanwhile, Beyoncé places two singles in the festive top ten, climbing to four with 'If I Were A Boy' and zooming to eight with 'Listen', the Dreamgirls ballad she sang with Burke on last week's X Factor final.
Peter Kay's alter ego Geraldine McQueen bows at five with yuletide offering 'Once Upon A Christmas Song'.
The top ten singles in full (click to read our reviews):
1. (1) Alexandra Burke: 'Hallelujah'
2. (30) Jeff Buckley: 'Hallelujah'
3. (1) Leona Lewis: 'Run'
4. (9) Beyoncé: 'If I Were A Boy'
5. (-) Geraldine McQueen: 'Once Upon A Christmas Song'
6. (18) James Morrison ft. Nelly Furtado: 'Broken Strings'
7. (2) Kings of Leon: 'Use Somebody'
8. (60) Beyoncé: 'Listen'
9. (5) Take That: 'Greatest Day'
10. (4) Britney Spears: 'Womanizer'
Source: Official Chart Company.
> Click here for the top ten Christmas albums