Maxi Gomez netted the opener in the 46th minute and then created the second for Iago Aspas in the 52nd as Atleti failed to recover from a poor first half in which its lacked cutting edge up front.
Antoine Griezmann sought to inspire his side, but a fightback never looked likely for Diego Simeone's men, who were tipped to put up a decent fight for the title this season.
Indeed, things went from bad to worse for Atleti as Stefan Savic saw red with 20 minutes remaining, although Gustavo Cabral was harshly denied a third by a marginal offside call after a VAR (video assistant referee) consultation.
After an open yet uneventful first 25 minutes in which the two sides took turns to counter, Griezmann was inches from firing Atleti in front as a 20-yard drive crept wide.
There was little incident of note in the remainder of a sweltering first half, but Celta took just 42 seconds to break the deadlock after the restart.
Gomez pounced on Diego Godin's slip to hammer low into the net and Atleti was quickly stunned by a second blow, the first goalscorer turning creator with a lovely delivery onto Aspas's head.
Savic was then dismissed for a second yellow card as he handled the ball to concede a free-kick from which Cabral thought he had added a third, before a lengthy VAR (video assistant referee) delay saw the defender judged offside.
Atleti will have to wait for its opportunity to bounce back. The international break means it is a fortnight before it faces Eibar in its next league match. Celta will travel to Girona two days later.