The home team made a bright start to the game and were rewarded in the 12th minute when Joan Capdevila put the ball in his own net to make it 1-0.
Juan Forlin came close to immediately replying for Espanyol, but his effort was seen off by the defenders.
Negredo had a chance to grab his second of the game two minutes before half time, but his shot was blocked by the defence.
Espanyol's Christian Stuani had the first chance of the second half, but his effort was well saved by the goalkeeper.
Sevilla continued to push forward and came close on two occasions through Rakitic and Alberto Moreno.
Moreno broke free again on 68 minutes, but he couldn't find the target with his effort.