Goals by Clarke Carlisle and Barry Nicholson either side of half time earned Preston a first League One win.
Chesterfield were caught cold from a set-piece when Carlisle rose to head home the opener.
The Spireites came close when Dean Morgan's on-target shot struck a defender and Mark Allott shot just past the post in the second half.
But Nicholson's looped header, from Brian McLean's cross, in the 70th minute ensured victory for North End.
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Chesterfield manager John Sheridan told BBC Radio Sheffield:
"I'm disappointed with the goals. They've had opportunities to score more but I think a big part of it was down to us, a lack of concentration, individual mistakes that just create problems.
"I think the second goal killed us as a team, but I do think we were trying to do the right things - we just didn't have that cutting edge.
"We'll stay together and we'll work very hard. We did try to get back into the game which was very pleasing for me."