Antoine Griezmann had the hosts’ best effort when he headed against the post early in the second-half, but Atletico failed to take advantage when Vitolo saw a second yellow card just after the hour mark.
A point means Atletico and Barcelona are now level on points at the top of the table ahead of their meeting at the Camp Nou next weekend.
Real Madrid can close to within two points of the leaders when Zinedine Zidane gets his first taste of action as boss away from the Santiago Bernabeu at Real Betis later on Sunday.
There had been just 17 goals in Atletico’s previous nine matches at home in La Liga this season and clear-cut chances were again hard to come by for both sides.
Greizmann just couldn’t stretch to turn Diego Godin’s header across goal in at the far post early on.
Meanwhile, at the other end, Sevilla’s best chance fell to Ever Banega but his deflected shot spun inches over the bar.
Griezmann was desperately unlucky when he timed his run to meet Koke’s cross perfectly just after the break only to see his bullet header come back off the post.
Atletico were gifted the initiative for the final half hour when Vitolo was shown his second booking for chopping down Luciano Vietto just outside the box.
The hosts still struggled to open up the Sevilla defence, but a well-worked free-kick freed Yannick Ferreira Carrasco inside the area and his fierce shot was brilliantly saved by Sergio Rico.
Rico also did well to turn Gabi’s piledriver over before Carrasco’s free-kick at the death was deflected behind as Sevilla held on for a point that keeps them in the race for fourth place, eight points adrift of Villarreal.
Earlier, Athletic Bilbao gunned down high-flying Eibar 5-2 in a Basque derby at San Mames.
On-loan Atletico striker Borja Baston scored twice for the visitors to take his tally for the season to 15.
However, two goals from Aritz Aduriz, Sabin Merino, Aymeric Laporte and a late Mauro dos Santos own goal moved Athletic up to eighth.
