The singer's Frankie Goes To Hollywood cover climbed five places to reach the top this week, knocking down 'Troublemaker' by Olly Murs to number three.
The track has been used in the latest John Lewis Christmas advert, and is the first such song to reach the top after Ellie Goulding hit number two with 2010's 'Your Song'.
It is also 28 years since the Frankie Goes To Hollywood original was a number one hit.
Bruno Mars stays at number two with 'Locked Out of Heaven', just 1,500 copies behind Aplin.
Labrinth's 'Beneath Your Beautiful' remains at number four once again, while Rihanna slips two to five with 'Diamonds'.
Pink climbs 18 places to eight with 'Try', following her X Factor appearance last week.
Pitbull enters at 16 with 'Don't Stop the Party', while Tulisa's latest single 'Sight of You' is new at 18. Burns sneaks in at 39 with the Otto Knows remix of new track 'Lies'.
A host of Christmas classics continue to rise and re-enter the chart, with The Pogues and Kirsty MacColl climbing 12 places to 15 with 'Fairytale of New York'.
Mariah Carey climbs ten spots to 20 with 'All I Want for Christmas is You', while Wizzard are at 31 with 'I Wish It Could Be Christmas Everyday'.
Wham! enter at 34 with 'Last Christmas', followed by Slade's 'Merry Xmas Everybody' at 35 and Band Aid's 'Do They Know It's Christmas' at 37.
Watch the video for Gabrielle Aplin's 'The Power of Love' below:
Source: Official Charts Company
> This week's albums chart