Sunderland were still refusing to lie down, with substitute Anthony Stokes bringing a fine save from Almunia and Jones shooting across the face of goal with the Arsenal keeper out of position following a fine run by Miller.
He lofted an effort towards goal with the Mexico keeper stranded out of position, but Francisco Javier Rodriguez was perfectly positioned on the line to clear the danger.
The Cottagers had a level of control over the game and Bobby Zamora set up Dempsey at the far post but his shot was blocked by Ian Ashbee with keeper Duke out of position.