Darren Purse headed the visitors in front but former Valiants striker Marc Richards silenced the 2,000 travelling Vale fans with a deflected free-kick and a sharp finish only for Pope to bag his 31st goal of the season in the 85th minute to salvage a point.
Vale went in front in the fifth minute when Purse was allowed to run across the face of goal to head a corner past Tommy Lee from eight yards.
But Chesterfield responded with two goals in the space of four minutes, with a 25-yard free-kick from Richards taking a big deflection to wrongfoot Chris Neal before the striker scored from a tight angle after Neal could only parry a Jay O'Shea shot.
Vale had been second best in the first half but they carried more of a threat after the break, Doug Loft lifting the ball on to the roof of the net in the 66th minute before his 20-yard shot was tipped over four minutes later.
But Vale's pressure told in the 85th minute when Pope's downward header squirmed under the body of Lee.