Jack Lester scored twice in six second-half minutes to become the first Chesterfield player for 80 years to hit 20 goals in consecutive seasons.
Vale had goalkeeper Joe Anyon taken off on a stretcher during a goalless first half before Lester broke the deadlock when he converted Drew Talbot's cross.
The striker then made it 2-0 with a deflected shot.
Paul Marshall's free-kick set up a tense final 14 minutes but Chesterfield held on for victory.
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