The track, which could be the first cut from her forthcoming seventh album, sees her addressing her addiction issues and admitting to a recent relapse after six years of sobriety.
It has thundered to the very top of the US iTunes listings, and also hit the Top 10 on the UK equivalent.
At time of writing, Sober is also No1 in on iTunes in Argentina, Brazil, Colombia, Cyprus, Ecuador, Greece, Guatemala, Hungary, Netherlands, Peru and Saudi Arabia.
The iTunes chart is not a country’s official singles chart, but does contribute significantly to it – with digital downloads from other stores, streams from sites such as Spotify and Apple Music, and physical sales also factoring in.
In some territories, such as the US, YouTube hits and radio plays are also contributors.
So we’ll have another week left before Sober impacts official weekly charts in various countries, but it’s an encouraging sign that it’s off to such a strong start on iTunes.
Interestingly, Lovato is at Number One on the UK iTunes chart – but not with Sober.
Instead it’s her Clean Bandit collaboration Solo that’s the best-selling song on the store at the moment; and the song is also reigning in Ireland.
Today the track is expected to be announced as the UK’s official Number One single for the week, having also performed strongly on streaming platforms.
At Monday’s midweek stage, it held a narrow lead over George Ezra – and the lead was still being maintained when another update was issued on Wednesday.
The UK chart week runs from Friday to Thursday, so the results of the last week will be confirmed today.
If Solo has held on, it will be Lovato’s first ever No1 in the UK, and Clean Bandit’s fourth.
Meanwhile, fans have been rallying around the 25-year-old following her raw delivery on Sober.
One fan wrote: “recovery is a daily battle. sobriety is a daily battle. relapse does happen. we are only human.
“No human can fight and fight and fight everyday to the fullest – everyone has got those days/weeks were we feel weak. but its important to get up and continuing to fight. #sober.”
Another tweeted: “I think what people don’t understand about addiction is that it is always there and it’s so easy to slip back into old habits.
“Demi no longer being sober does not take away the 6 years that she was, she’s so strong. She will get through this. #SOBER.”
Sober by Demi Lovato is out now.