Centre back Victor Laguardia's fourth-minute header from a Ruben Duarte corner was enough for the hosts to secure their first win of the season as they moved off the foot of the table.
The result left Diego Simeone's side second on 14 points, two behind leaders Real Madrid, who are in action later on Saturday when they host Villarreal.
"We need to improve and ensure that our games are more consistent, because right now they really aren't," Simeone said.
"It's always tough when the opposition closes up shop. We didn't have the kind of speed or skill needed to undo them.
"The most important thing for us is to improve and grow and I'm confident we're heading in the right direction with the work we're doing."
Atleti huffed and puffed as they attempted to find a way back into the match after such an early blow, but were kept out by admirable defending from the hosts.
Marcos Llorente, Luis Suarez and substitute Angel Correa all went close for the visitors and Laguardia headed Kieran Tripper's shot off the line.
Tomas Pina missed a glorious chance to double Alaves's lead nine minutes from time, but fired over when unmarked on the penalty spot - but his side hung on to claim a first victory over Atleti since 2003.