The pairing follows Harris's remix of Florence and the Machine's 'Spectrum' in topping the UK chart, knocking Swedish House Mafia's 'Don't You Worry Child' down to two.
It is the electronic producer's fifth number one single in the UK either as a solo or featured artist.
Psy's 'Gangnam Style' is a non-mover at three, with Rihanna also staying at four with 'Diamonds'. Adele drops three places to five with her Skyfall theme of the same name.
Lawson's latest single 'Standing in the Dark' lands at six, while Taylor Swift's 'We Are Never Ever Getting Back Together' climbs back up five places to seven.
Maroon 5 leap ten spots to eight with 'One More Night', with Conor Maynard and Ne-Yo dipping one place to nine with 'Turn Around'. Flo Rida also falls one with 'I Cry' to ten.
Rebecca Ferguson enters at 15 with her new single 'Backtrack', while The Voice UK finalist Tyler James grabs a new entry at 28 with 'Single Tear'.
One Direction fall ten places to 16 with 'Live While We're Young', with Disclosure climbing nine spots to 17 with 'Latch'.
Justin Bieber and Nicki Minaj leap 80 places to 20 with their duet 'Beauty and the Beat', while albums chart-topper Jake Bugg climbs 53 places to 33 with 'Two Fingers'.
Taylor Swift continues her run of Top 40 hits from her latest album Red, with 'State of Grace' landing at 36.
Everything Everything score their first Top 40 hit so far, with new single 'Cough Cough' entering at 37.
John Denver re-enters at 38 with his classic love tune 'Annie's Song', after its use in a TalkTalk advert.
Watch the video for Calvin Harris and Florence Welch's 'Sweet Nothing' below:
Source: Official Charts Company
> This week's albums chart