Atletico Madrid have climbed up to second in the La Liga table, but missed the chance to take top spot.
Barcelona's dropped points in the earlier kickoff provided the Rojiblancos with the opportunity to overtake the Catalan giants and rivals Real Madrid.
Despite taking the lead against Sevilla, Madrid failed to hold on to their advantage and remain behind leaders Barcelona on goal difference.
Atletico came close again moments later, this time through striker Diego Costa, who turned on the edge of the area before firing into the side-netting.
The hosts did eventually get the breakthrough after 18 minutes through Villa, who latched onto a loose ball and fired into the bottom corner.
Captain Ivan Rakitic stepped up and thumped his penalty into the bottom corner to level the contest.
As the clock ticked towards full time, Alberto Moreno was shown a straight red card for the visitors, but Sevilla held on to maintain their unbeaten run that now stretches to eight games.
Ateltico, meanwhile, will rue their missed opportunity to climb to the top of the table.