Atletico caught the Celta defence napping inside two minutes when Rodrigo Riquelme played a quick free-kick through to Angel Correa, but goalkeeper Vicente Guaita was alert to the danger and made the save.
And Guaita was the visitors’ saviour twice more inside the first 15 minutes, reacting quickly to efforts from Riquelme and Samuel Lino.
Defensive resilience at both ends prevented any clear-cut opportunities until five minutes before the break when Koke played a long ball forward and into the path of Marcos Llorente, who brought the ball down well but struck a tame effort straight at Guaita.
After mustering one shot off target all half, Los Celestes came close to taking the lead in stoppage time, when Jonathan Bamba’s cross deflected off Axel Witsel’s back and looped over the bar.
After the interval, Diego Simeone turned to substitute Alvaro Morata to provide a focal point for the Atleti attack, and it took just 14 seconds of the second half for him to register an effort, heading Cesar Azpilicueta’s cross just wide.
Los Colchoneros were hoping that was a sign of things to come, but it was the visitors who generated the next big chance when Bamba cut the ball back to Iago Aspas, who stung the gloves of Jan Oblak just before the hour mark.
As full-time drew ever closer, both sides traded chances, with Memphis Depay testing Guaita at the near post before the shot-stopper denied what would surely have been a goal-of-the-season contender. Rodrigo de Paul was the would-be architect, chipping the ball forward to Pablo Barrios, who connected with a flying volley from an impossible angle that the former Crystal Palace man tipped onto the crossbar.
Five minutes from time, however, the winner arrived for the hosts. Having been denied an assist, De Paul took matters into his own hands when a corner was cleared to him on the edge of the area. He controlled the ball with his chest and volleyed it into the top corner, putting Atleti just one more win away from a guaranteed top-four berth, while keeping alive their chances of a podium place for the 13th season running.
Flashscore Man of the Match: Rodrigo de Paul (Atletico Madrid)
