At least one supporter is believed to have been seriously injured in the incidents that took place close to the ground.
The Spanish football league said in a statement it had tried to postpone the game at the last minute, but it hadn’t been possible.
On the field, Atletico once again relied on their expertise from set-pieces to claim all three points as Saul Niguez headed in from Koke’s free-kick just before half-time.
And Arda Turan’s deflected effort doubled their advantage 10 minutes after the break as Deportivo could only clear a corner to the edge of the area where the Turkish international was lurking.
Victory takes Atletico a point ahead of Barcelona and back to within four points of leaders Real Madrid, but Barca can reclaim second spot when they visit Valencia later on Sunday.
Atletico started much the brighter despite the understandably subdued atmosphere at the Vicente Calderon and could have been in front twice in the opening 10 minutes.
Mario Mandzukic scored his first hat-trick for Atletico in the 4-0 mauling of Olympiakos in midweek and was inches away from finding the net again when he headed Koke’s fine cross on to the post.
Two minutes later another delivery from Koke caused havoc as Jose Gimenez nodded his corner towards goal, but Sidnei was on hand to hack the ball clear off the line.
Atletico Madrid’s Croatian forward Mario Mandzukic heads the ball during the Spanish league football match Club Atletico de Madrid vs RC Deportivo de la Coruna at the Vicente Calderon stadium in Madrid on November 30
The visitors were finally punished from a set-piece two minutes before the break as Koke’s in-swinging free-kick was flicked on by Diego Godin and the unmarked Niguez powered home a header at the back post.
Turan then made the game safe with Atletico’s first effort on goal in the second-half as he pounced on a loose ball at the edge of the box and Ivan Cavaleiro inadvertently deflected the ball beyond the helpless Fabricio in the Deportivo goal.
Atletico then took their foot off the gas in the final half-hour, as Diego Simeone replaced Mandzukic and Antoine Griezmann with a third home win in a week assured.
However, substitute Cristian Rodriguez was inches away from adding a third when he shot just wide nine minutes from time.