Second-half goals from Yannick Carrasco and Antoine Griezmann were enough to beat Eduardo Berizzo's men and lift the hosts above them in the table.
Both sides held an unbeaten record this season heading into the showdown in the capital and there was a distinct wariness to proceedings, with Pablo Sarabia and Filipe Luis hitting the woodwork with the only real chances of the first half.
Carrasco made the most of a defensive error from Steven N'Zonzi to put Atleti in the lead soon after the interval, though, and Sevilla rarely looked like mustering a comeback against a team they have beaten only once in 14 league meetings.
Griezmann's emphatic finish in the 69th minute made the points safe and allowed head coach Diego Simeone to hand his stars some rest ahead of next week's Champions League meeting with Chelsea, as imminent new signing Diego Costa watched on approvingly from the stands.
They are now a point clear of Sevilla in the table and just one behind Barca, who face Girona in a derby match later on Saturday.
Atleti applied some early pressure but Sarabia came close to breaking the deadlock in the 12th minute, his shot taking a deflection off Stefan Savic before bouncing off the right-hand post.
Filipe Luis rattled the woodwork himself midway through the half, blasting a half-volley off the crossbar after being teed up by Carrasco's cut-back, as Atleti began to threaten in earnest.
The hosts continued to look the more likely to find a breakthrough but lacked any real verve in the attacking third, as Sevilla dealt comfortably with a succession of corners and kept clear-cut chances to a minimum.
However, less than two minutes into the second half, Atleti made the visitors pay for their first defensive lapse. Carrasco chased down a loose ball, dispossessed N'Zonzi and rounded Sergio Rico before slotting home.
With their noses in front, Atleti seemed content to sit back and allow Sevilla the ball, although they invited one dangerous-looking scramble in the box that almost allowed Luis Muriel a tap-in at the left-hand post.
But Atletico pounced on more slack defending to make the win safe with a little over 20 minutes left to play. Griezmann made a fine sliding tackle to block Jesus Navas' attempted clearance in the penalty area, and when he received the ball back from Filipe Luis, he blasted low past Rico and into the bottom-right corner.
Atleti eased through the closing stages to claim an important three points that puts pressure on leaders Barca, as well as champions Real Madrid, who are six points further back in the standings with a game in hand.
Key Opta stats:
- Yannick Carrasco has scored 13 goals in LaLiga since the start of last season, more than any other midfielder.
- It is third time the Belgian player has scored in back-to-back LaLiga games since he joined Atletico.
- Sevilla have failed to score for the first time this season in all competitions.
- Antoine Griezmann has had a hand in five of Atletico's last seven goals against Sevilla (two goals, three assists).
- Atletico have not lost any of their last ten LaLiga games (W7 D3), their best streak since May 2015 (13)
- Under Simeone, Atletico have not lost a LaLiga home game against an Andalusian side (W23 D3).
- Atletico are unbeaten all the 13 LaLiga games in which Carrasco scored at least once (W12 D1)
- Diego Simeone has only lost one of his seven games as a manager against Eduardo Berizzo in LaLiga (W5 D1). This was in February 2015 - a 2-0 loss at Baladdos.