Angel Correa looked sharp for the hosts on his return from suspension and, in the 15th minute, a penetrating run saw him breeze beyond two players and into the box, where he went down under a challenge from Ander Capa that the referee deemed to be legal.
Thomas Partey was booked for a high challenge as the match became increasingly physical and dogged, but Atletico continued to look the more threatening.
Antoine Griezmann blazed a shot over from the left-hand side of the box after a great cross-field pass from Jesus Gamez after 19 minutes.
Jose Luis Mendilibar’s side were blunted by the absence of their top-scorer Borja Baston – ineligible against his parent club as part of his loan deal – and they struggled to create chances, despite a decent amount of possession.
Correa and Jota missed chances at either end as neither goalkeeper was forced into a save before half-time, but, within a minute of the restart, the deadlock was broken.
A slip from Saul was pounced upon by Sergi Enrich, who squared for Keko to fire into the top corner.
Disappointed with his team’s response, Simeone had Oliver Torres and Luciano Vietto ready to come on from the bench.
However, before the duo could be introduced, a series of Atletico corners culminated with Gimenez heading in the equaliser in the 56th minute.
Vietto and Oliver were brought on soon afterwards, but it was another defender who added to Atletico’s tally.
Saul atoned for his earlier error by rising highest to steer Koke’s corner beyond Asier Riesgo, who was unable to keep the shot out despite getting a hand behind it.
Torres was introduced after 76 minutes in place of Ferreira Carrasco and after Vietto had seen a goal ruled out for a marginal offside decision, the striker steered home from the Argentine’s cross to complete the scoring and celebrate his personal landmark.