A lively start saw the visitors take the lead after three minutes when Phil Picken's cross was dropped at the front post, leaving Jamie O' Hara to tap home from close range.
The response was quick with Jeff Smith's in-swinging corner from the right being met by George Pilkington, who had no problems in heading past a stranded Barry Roche.
The Valiants struck again on the quarter-hour mark when another Smith corner caused havoc in the box, with Pilkington popping up again to finish with his right foot from two yards.
Youngster Joe Cardle almost lit up Vale Park five minutes before the break when his tricky run took him past three Chesterfield players, only for the winger to miss the target from 14 yards.
The Spireites went in search of an equaliser six minutes after the restart when Picken swung in a long ball from the right, but substitute Wayne Allison failed to capitalise, smashing the ball into the side-netting.
The visitors went close again in the 55th minute when goal scorer O'Hara saw his low drive parried by Mark Goodlad, with any further danger being averted by Pilkington's clearance.
O'Hara looked like the main threat to the home side's lead when his 30-yard free-kick struck the outside of Goodlad's right post.
The woodwork was rattled again in the 66th minute when Aaron Downe's header across the face of goal was met by Allison, who volleyed the ball against the same post.
The match was put beyond doubt nine minutes from the end when Cardle's defence-splitting throughball fed Michael Cummins for a superb finish from 12 yards.