Barcelona's 2-1 win at Malaga on Saturday had seen the Catalan outfit rise above Atletico at the summit and Diego Simeone's side have missed the chance to reclaim first spot ahead of their trip to Camp Nou next weekend.
A tight opening to the match saw Sevilla force the first half-chance, but Adil Rami's header from close range dropped wide of Jan Oblak's post, before Gabi struck one wide of the goal down the other end.
Saul Niguez was next to come close in the 14th minute after driving into the Sevilla box, but the midfielder's effort hit the side-netting as both teams continued to exchange possession in a tense opening to events in the capital.
Grzegorz Krychowiak and Coke then took it in turns to head over the Atletico crossbar, but the best chance of the opening 25 minutes came to Antoine Griezmann. Juanfran did well to set up the Frenchman with a low cross, but the attacker turned wide of the post from close range.
Gabi seemed keen on trying his luck from long range throughout the match and had one more sighter during a period where Atletico were in control of the possession against a physical Sevilla side.
Griezmann had another opportunity 10 minutes before the break after a fine set-up from Diego Godin, but once again he missed the target from close range.
Sevilla came close to making the breakthrough in the 36th minute when Sergio Escudero set up Ever Banega with a clever pass, but the Argentine's effort was deflected onto the crossbar and behind, before Oblak kept out a low strike from Coke in the final stages of the first period.
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Griezmann had the first serious chance of the second period when he met a cross from Koke, but the attacker hit the post with a well-placed header as Sevilla kept the score level.
Sevilla continued to hold out as the match approached the hour mark, but they were reached to 10 men in the 61st minute when Vitolo picked up a second yellow for a poor challenge on Luciano Vietto. In protesting, Sevilla boss Unai Emery was also sent to the stands as it got worse for the visitors.
Gabi then tested Rico with a stinging effort in the final 10 minutes as Sevilla dropped deeper and deeper to defend their own box. The visitors managed to hold on, however, to secure a vital point in the Spanish capital.