Victor Laguardia scored with a header off a corner four minutes into the match, giving Alavés its first points of the season and preventing Atlético from regaining the league lead.
Atlético stayed in second place, two points behind Real Madrid, which hosts Villarreal later Saturday. Atlético had been unbeaten in seven matches in all competitions this season. The home victory kept Alavés from equaling its worst-ever start to the league.
It had started with six straight losses in 2017-18. Alavés hadn’t beaten Atlético in the league since 2003, with eight losses and four draws in that span. The only team left without a point to start the season is Getafe, which visits Real Betis on Sunday.