Preston, haunted by nine successive playoff failures, completed a 4-0 aggregate success with a comfortable victory in the second leg at Deepdale.
The final flourish came in the 87th minute when former Everton striker Beckford spotted Chesterfield keeper Joe Murphy off his line and took aim from inside his own half to send a shot arcing perfectly into the net.
Beckford, who netted the only goal in the first leg, also opened the scoring in the return when he rolled a defender to fire home in the 38th minute.
Joe Garner added a second goal from the penalty spot in the second half after Murphy rushed off his line to bring down Daniel Johnson.
Preston, who had exited at the semi-final stage of the playoffs six times since 1989, will face the winners of Sheffield United's clash with Swindon Town in the final on May 24 for a place in the Championship (second tier).
(Reporting by Toby Davis; editing by Ed Osmond)
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