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The visitors made an attacking start as they tried to overturn their 1-0 deficit from the first leg, but Sam Clucas's shot inside the opening 10 minutes was well blocked on the line.
Joe Murphy started in goal for Chesterfield, having joined on an emergency loan from Huddersfield Town earlier this weekend, and he had to be alert when Sam Hird squared the ball to Paul Gallagher, but the keeper made a comfortable save.
Preston made the most of those missed opportunities shortly before the break when a quick move from Joe Garner set up Jermaine Beckford to hit the ball on the turn in the box, volleying past Murphy to double the home side's aggregate lead.
Chesterfield came out all guns blazing at the start of the second half as they desperately tried to keep their promotion hopes alive, but Gallagher was on hand to clear a Tendayi Darikwa effort after the midfielder appeared to be clean through on goal.
The Spireites continued to dominate possession in the opening 15 minutes of the second half, but they were caught out by a quick counter-attack from Daniel Johnson, resulting in Murphy conceding a penalty as he rushed off his line to halt the Preston man's run.
Garner stepped up to take the spot kick, and doubled Preston's lead on the day with a clinical finish into the top corner, leaving Murphy with no chance.
Garner tried to add his second shortly after when he attempted to catch Murphy out with a long-range effort, but the keeper watched it all the way.
Chesterfield thought that they had a goal back inside the final 15 minutes when Jay O'Shea beat Johnstone with a header from a corner, but the crossbar came to the keeper's rescue, deflecting the ball clear.
Preston sealed the victory in style with just a couple of minutes remaining as Bailey Wright slid the ball through the middle to Beckford, setting the striker up for a drive from just inside the Chesterfield half into the bottom left corner.
Simon Grayson's side will face the winner of the tie between Swindon Town and Sheffield United for a place in the Championship at Wembley later this month.