Reds manager Billy Davies was up against his former side, who frustrated the Championship promotion hopefuls with an organised defensive display and then nearly snatched victory late on.
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Paterson, who scored a hat-trick in the third-round thrashing of West Ham United, fizzed a shot from distance narrowly wide of the post after cutting in from the wing, while Cox forced North End stopper Declan Rudd into a smart save with a powerful shot on the turn on nine minutes.
Jamie Mackie's shot over the crossbar on 38 minutes, following good work from Gonzalo Jara on the right, proved to be their last real sight of goal, but Preston were much more threatening after the break.
Darlow remained in the action up until the last kick of the game when he saved from Josh Brownhill's set piece, as Simon Grayson's League One visitors earned a second chance to progress back at Deepdale.