Sevilla, who have lost four of their last five league games prior to this evening's clash, saw another big opening squandered shortly before the half-hour mark when Iborra's attempt at the end of an Ever Banega cross clipped the post on its way through.
Moya was the busier of the two goalkeepers as the first half wore on, with Los Rojiblancos having the better of the half-chances, but they were ultimately unable to find a way through in a goalless opening 45 minutes at the Ramon Sanchez Pizjuan.
After a flurry of bookings at the start of the second half, Banega's free kick met the head of Alejandro Arribas, but Moya saved well.
Torres came close to scoring in the closing stages, but his shot went wide of the right post.
Atletico remain third in the La Liga table, whilst Sevilla stay in fifth.