Diego Simeone's side stay second but are equal on 23 points with Sociedad with a game in hand on the leaders thanks to Toni Lato's own goal 11 minutes from time.
Stingy Atletico have conceded just twice in their nine league matches so far this season and have only scored two less than La Liga top scorers Sociedad, who host third-placed Villarreal on Sunday.
Atleti's win at the Mestalla, which came without Luis Suarez following the striker's positive Covid-19 test earlier this month, puts them four ahead of Villarreal and six in front of reigning champions Real Madrid, who face Alaves in Saturday's late match.
Fellow traditional title rivals Barcelona are 12 points back in 13th place, although they host Osasuna in Sunday's early match and will still have two games in hand on Sociedad come the end of the weekend.
Atletico will face European champions Bayern Munich in the Champions League on Tuesday hoping to reach the knockout stages with a match to spare.