Vitolo cashed in from poor positioning from Valladolid's debutant goalkeeper Jose Antonio Caro to head the ball just over the goalline. Although it was headed away by a defender, a VAR review ratified the linesman's decision to award the goal.
Playing for the first time without fans at the Wanda Metropolitano, Atletico lacked the fluidity they showed in their 5-0 thrashing at Osasuna last Wednesday and were fortunate not to go behind as Valladolid impressed in the first half.
The victory took Atletico on to 52 points after 30 games, level with fourth-placed Sevilla, but gave them a four-point cushion over fifth-placed Getafe to further boost their chances of a top-four finish and Champions League qualification.
Valladolid are 15th on 33 points, seven points above the relegation zone.