Valladolid produced with a disciplined yet bold performance and could have taken an early lead when Kenan Kodro headed against the bar, while Roque Mesa had two clear sights at goal from outside the box but failed to hit the target each time.
Barca came close to scoring right before halftime when their former goalkeeper Jordi Masip palmed a strike from Pedri on to the post. The keeper thwarted Dembele in the second half and then watched on in relief as Antoine Griezmann headed the rebound just wide.
The Catalans were dealt a helping hand when Valladolid's Oscar Plano was sent off in the 79th minute for a challenge on Dembele. They finally took advantage when the French forward caught a loose ball in the air with his left foot, slamming it inside the near post.
A sixth consecutive league win for Ronald Koeman's side took them back into second place and moved them on to 65 points, two above third-placed Real Madrid and one behind Atletico, who were beaten 1-0 at Sevilla on Sunday.