A goal from substitute Vitolo with nine minutes remaining gave Diego Simeone’s side the three points.
They now have 52 points and a four-point edge over Getafe in their Champions League pursuit after winning for the first time behind closed doors at their Wanda Metropolitano stadium.
Vitolo had come on as a substitute after 73 minutes for Marcos Llorente and grabbed the winner with a header from a corner after Valladolid keeper Juan Antonio Caro had failed to clear.
Getafe’s hopes of finishing in La Liga’s top four took another knock as their disappointing return from the three-month coronavirus suspension continued with a 1-1 draw at home to Eibar.
Peter Etebo’s smart finish put Getafe in front at the Coliseum Alfonso Perez before Eibar’s Charles equalised from close range on the stroke of half-time.
Eibar might even have snatched victory, only to have a late goal from Pedro Bigas ruled out for offside.
Getafe have now taken just two points from three games since the restart.
“It’s clear we needed to win to give us a boost,” said Getafe’s Jaime Mata.
“It would have kickstarted us after the break but we have to keep fighting until we get that win. People say our ambitions are too high but we are going to keep fighting.”
Getafe are punching above their weight towards the top of the table, having enjoyed a remarkable four years under coach Jose Bordalas.
They were only promoted to the top tier in 2017 and missed out on Champions League qualification on the final day last year, edged out by Valencia.
But their challenge may not extend so far this term given this draw followed a stalemate at home to struggling Espanyol and defeat by Granada.
It contributes to a more prolonged dip in form that has included only two wins in nine.
Eibar are without a victory themselves in five matches but this was a valuable point that gives them something to build on in their battle to avoid relegation. They sit 16th, three points above the bottom three.
With their coach Jose Luis Mendilibar serving a touchline ban, Eibar fell behind after half an hour when Marc Cucurella’s deep cross was volleyed back in by Angel Rodriguez and Etebo steered the ball first time into the corner.
But Eibar responded and when Getafe’s defence failed to push out together after a botched Eibar free-kick, Bigas was left free to nod across to Charles, who had a simple finish.
Neither team really deserved to win it in the second half but Eibar thought they had when Pape Diop’s cross grazed the top of Bigas’ head and bounced in. But Bigas had strayed just offside and Eibar had to settle for a point.
Earlier, Espanyol were beaten 3-1 at home by Levante, a blow to their morale after they resumed with an impressive win over Alaves and hard-fought draw against Getafe.
Espanyol stay bottom, three points adrift of safety.
Athletic Bilbao climbed to ninth after Inigo Martinez’s flicked finish was enough to beat Real Betis 1-0.
Betis’ Sergio Canales missed an 85th-minute penalty in the defeat, which leaves coach Rubi on the brink of the sack.
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