Saul and Arda Turan grabbed the goals at Vicente Calderon in Sunday's clash as Diego Simeone's men triumphed for the 11th time in 13 games.
The action began on time despite violence between fans, which saw La Liga's ruling body, the LFP, make unsuccessful attempts to postpone the game.
Atletico subsequently condemned the incidents in a statement, saying "the values that promote the sport should prevail over any rivalry and together we must fight against the scourge of violence".
When the focus returned to the field, it was Atletico who made the better start as a good first-half performance ended with Saul heading home just before the break.
They grabbed a second 11 minutes after the resumption, Turan marking a fine performance by finding the net.
That proved enough for Atletico to secure the spoils, although many thoughts remained on the off-field troubles amid reports of a fan being hospitalised.
The added emphasis placed on attacking by Atletico this season was immediately in evidence as they produced fine flowing football during the opening exchanges.
And they almost opened the scoring in just the eighth minute, Koke sending in a pin-point centre that Mario Mandzukic superbly headed off the inside of the post.
Set-pieces, in particular, were causing problems as Deportivo defended desperately amid some fine deliveries from the impressive Koke.
But the visitors began to show the kind of resolute defending that has earned four clean sheets in their last five outings as the half wore on.
Their resistance was broken in the 43rd minute, though, as Atletico's mastery from set-pieces again showed itself.
Koke sent in the perfect free-kick to the front post, where Mandzukic flicked on for Saul to head into the unguarded net.
Simeone's side did not have to wait as long for a goal in the second period as Turan doubled the advantage.
Again a Koke set-piece proved decisive, his corner being cleared into the path of Turan - whose powerful effort was deflected into the net by Modibo Diakite.
The Turkish winger continued to shine and almost set up a third soon after, jinking his way down the wing and sending in a solid cross that Saul headed into the hands of Fabricio.
Deportivo were suddenly looking like a beaten side as Atletico continued to create openings, substitute Cristian Rodriguez spurning a great one when volleying narrowly wide.
Even the absence of a third goal did not have an impact, however, as the home side saw the game out comfortably.
