Valencia are now just a point adrift of third-placed Atletico after they comfortably saw off David Moyes's Real Sociedad 2-0 thanks to a double from Pablo Piatti.
Real Madrid can restore a four-point lead at the top over Barcelona and move nine clear of Atletico when they host Villarreal later on Sunday.
Sevilla and Atletico had suffered differing fates in European games in Germany in midweek as Sevilla progressed to the last 16 of the Europa League with victory over Borussia Monchengladbach, whilst Atletico lost 1-0 to Bayer Leverkusen in the first leg of their Champions League last 16 tie.
And the toil taken by those matches showed in a tense game short on clear-cut chances.
Sevilla had the better of the first period as Vicente Iborra struck the post and Miguel Angel Moya in the Atletico goal made a couple of smart stops.
However, the introduction of Koke and Fernando Torres from the bench gave the visitors a boost after the break.
Torres nearly sparked the breakthrough with a purposeful run and cross that was just behind the late arriving Griezmann and his fluffed finish was easy for Sergio Rico.
The former Liverpool and Chelsea striker then passed up a clear opening of his own when he placed a weak shot too close to Rico.
Torres then sent another shot wide as Atletico threatened on the counter-attack, but they were nearly caught out when Vitolo fired wastefully over from a well-worked corner six minutes from time.