The track - which features Florence Welch - debuts at number two on the tally, held off from pole position by Psy's 'Gangnam Style', which continues its lead at the top for a fourth week.
Meanwhile, Delta Goodrem enters at number seven with 'Wish You Were Here', Sam and the Womp leap 12 to nine with 'Bom Bom', and Taylor Swift's 'I Knew You Were Trouble' vaults 24 to 10.
Further down the chart, Swedish House Mafia lift 13 to 11 with 'Don't You Worry Child', Reece Mastin bounds 31 to 16 with 'Rock Star', and David Guetta holds at 17 with 'Play Hard'.
Kid Cudi is new at 32 with 'Just What I Am', Enrique Iglesias debuts at 33 with 'Finally Found You', and Little Mix's 'Wings' enters at 34.
Elsewhere, Justin Bieber and Nicki Minaj are at 40 with 'Beauty and a Beat', Swift's 'State of Grace' lands at 44, and Flume begin at 49 with 'Holdin On'.
The top ten singles appear below (click for our reviews where possible):
1. (1) Psy: 'Gangnam Style'
2. (*) Calvin Harris ft. Florence Welch: 'Sweet Nothing'
3. (2) Guy Sebastian ft. Lupe Fiasco: 'Battle Scars'
4. (3) Birdy: 'Skinny Love'
5. (4) The Script ft. will.i.am: 'Hall of Fame'
6. (6) Pink: 'Try'
7. (*) Delta Goodrem: 'Wish You Were Here'
8. (8) Rihanna: 'Diamonds'
9. (12) Sam and the Womp: 'Bom Bom'
10. (24) Taylor Swift: 'I Knew You Were Trouble'
Watch Calvin Harris's 'Sweet Nothing' video below: