The hosts struggled to create many chances in the first half and were denied shortly before the break when Valladolid keeper Jordi Masip went down and to his right to steer a well-hit Pedri shot off the post.
Lionel Messi fired just wide of the post on 70 minutes as Valladolid continued to frustrate Barcelona with time running out for Ronald Koeman’s side as they looked to pick up a crucial three points in the title race.
Barca were given the upper hand for the last 10 minutes of the match when Vallodild’s Oscar Plano was sent off with a straight red following his foul from behind on Dembele.
With time running out, Dembele pounced on a loose ball at the far post and hit a low volley past Plano to move his side up to 65 points from 29 games, one behind Atleti with nine games left to play in the season.
Real Madrid, who are in third place in La Liga on 63 points, host Barcelona in another edition of the Clasico on April 10 in a crunch match for both team’s title hopes.