Atletico are now level with Barcelona at the top of the LaLiga standings on 38 points from 17 matches, moving above Real Madrid who are third on 37. Barcelona host lowly Leganes later on Sunday.
Atletico, who have won all their games since late October, dominated proceedings throughout and created several opportunities but had to dig deep to break the deadlock, with their winner coming in a collaboration between two substitutes in the 69th minute.
Fullback Nahuel Molina lifted a long cross from the right touchline which found the unmarked Sorloth whose header at the far post beat goalkeeper David Soria.
After constantly rotating his selection and trying different formations over the first few months of the season, Atletico manager Diego Simeone seems to have finally found the starting line-up he is most comfortable with.
He sent out the 11 players who easily beat Slovan Bratislava 3-1 in the Champions League on Wednesday, with Antoine Griezmann and Julian Alvarez up front and two four-man lines in midfield and defence instead of the conservative fiveman defensive line he has been known for.