Diego Simeone's men were made to work for their victory, with Celta more than a match in most areas for the hosts in the first half, but it could not keep up in the second.
Angel Correa gave Atletico the lead in the opening 10 minutes, before De Paul's deflected effort early in the second half and a superb run and finish from Yannick Carrasco confirmed the win.
Substitute Gabriel Veiga pulled a goal back for the visitors, but an own goal from Unai Nunez ended any hopes for them.
Jan Oblak missed out for Atletico, despite playing in the dramatic midweek Champions League victory against Porto after suffering a knock at Real Sociedad last weekend.
Ivo Grbic deputised and was called into action after just a minute as a long ball was misjudged by Mario Hermoso, allowing Jorgen Strand Larsen in on goal, but the Norwegian could not beat the goalkeeper, who also had to save a Hugo Mallo header from point-blank range from a corner shortly after.
After surviving those scares, Atletico was ahead in the ninth minute after a fine one-touch move down the right as a cross-field ball from Reinildo to Nahuel Molina led to a cushioned pass to De Paul, who immediately slid the ball across to Correa to fire into the roof of the net.
The game calmed down after that, and it took until early in the second half for Atletico to double its lead as a Carrasco cross found substitute Koke, who laid the ball back to De Paul and his shot from the edge of the box deflected in off Nunez, wrong-footing the helpless Agustin Marchesin in the Celta goal.
Carrasco made it three in the 66th minute after picking the ball up on the halfway line and dribbling towards the penalty area, cutting in from the left before moving back onto his left foot and firing past Marchesin at the near post.
Celta got a goal back with 19 minutes remaining as a throughball from Iago Aspas down the right found Veiga, whose shot squirmed under Grbic, but the contest was over when Cunha raced past Nunez, before hitting a cross that deflected in off the visiting defender.