The tall striker struck on 35 minutes and 88 minutes to stretch Preston's unbeaten run to 23 matches after Darren Ward had fired Palace in front on 26 minutes.
A lively cup tie soon snapped into action with Gabor Kiraly being forced to make a dramatic save from his own player as Ward saw his header loop over the Hungarian keeper. Kiraly managed to bend backwards to palm the ball away for a corner.
Then at the other end Jobi McAnuff released Andy Johnson but Chris Lucketti made a crucial tackle as the Palace hit-man accelerated into the penalty area. Palace appealed for a penalty but the referee would have none of it.
It was end-to-end stuff but the Eagles opened the scoring on 25 minutes. McAnuff's inswinging corner was followed by Ward who easily steered the ball past Carlo Nash from ten yards out.
But the lead lasted just 11 minutes as Dichio at last broke his barren 22-match spell with a neat header from close range from Paul McKenna's free-kick.
After the break, the tie became somewhat scrappy but Preston were getting stronger by the minute.
The Eagles were making little impact and seemed to have dropped a gear after their impressive performance in the first 45 minutes.
Nash had a relatively comfortable time although McAnuff did manage to test him with a 15-yard shot which the former Palace custodian saved at the far post.
Preston were however enjoying good deal of possession and it eventually paid off two minutes from time.
Another free-kick from McKenna landed inside the goalmouth and, as both Mark Hudson and Kiraly hesitated, Dichio took advantage with another neat header to earn Billy Davies' side a home tie against the winners of Wednesday's replay between Coventry and Middlesbrough.