The champions took an early lead through Koke's deflected long-range effort and Saul headed home from a typically brilliant set-piece move three minutes before half-time.
Atleti's fourth win of the campaign, which leaves them two points behind leaders Barcelona, was rounded off by late goals from Raul Garcia, who converted an 83rd-minute penalty, and Raul Jimenez.
Sevilla struggled to create any clear-cut chances as they suffered a first defeat of the season on a difficult evening in the capital.
Much talk surrounded the return of Atletico boss Diego Simeone to the dugout, with the Argentinian having served a lengthy touchline ban following his conduct during the second leg of the Supercopa de Espana last month.
Simeone's return coincided with that of striker Mario Mandzukic, who regained his place in the side after a recovering from a broken nose.
The Croatian, donning a protective face mask, was predictably at the centre of the home side's attacking efforts during a tightly contested opening, but struggled to find the space needed to create any clear-cut opportunities.
Sevilla came into the game having not won a league game at the Vicente Calderon in six years, and their attempts to end that record were dealt a substantial blow after 19 minutes.
A speculative long-range strike from Koke on the edge of the area struck the ankle of Nicolas Pareja, causing the ball to loop over the head of goalkeeper Beto and into the net.
Simeone's men nearly doubled their lead seven minutes later, with Beto on hand to tip a free header from Gabi over the bar, before Cristian Ansaldi fired wide.
Atletico eventually gained further reward when a well-worked set piece fell to Miranda on the edge of the box and his wonderfully controlled volley to the back post found the head of Saul, who made no mistake from six yards.
Sevilla boss Unai Emery threw on Denis Suarez and Ever Banega at half-time in an attempt to boost his side's creative threat but the hosts remained largely untroubled, with visiting striker Carlos Bacca starved of quality service.
Atletico should have clinched the win in the 66th minute when Junfran was allowed to cut inside from the right and clip the ball into Mandzukic, whose powerful header was parried away by Beto.
The Portuguese stopper was on hand again just a minute later to keep out Raul Garcia's stinging volley, but could do nothing about Atleti's late strikes.
A high boot from Diogo Figueiras brought down substitute Antoine Griezmann inside the area and Raul Garcia confidently stroked the resulting spot-kick into the bottom-left corner.
An excellent night for Simeone and the home faithful was completed when Koke provided a teasing cross that substitute Jimenez converted with a diving header.