Peterborough were two-nil up at half-time following goals from Josh McQuoid and Shaun Brisley. Eoin Doyle pulled a goal back early in the second half but Britt Assombalonga's 77th minute penalty sealed it for the Posh.
The match was only a few minutes old when Doyle went down in the area under a challenge from Brisley and Chesterfield's penalty appeals were waved away.
Peterborough took the lead in the seventh minute when McQuoid followed up to score after Tommy Lee could only parry Michael Bostwick's header after a corner.
Paul Cook was forced to make a change in the 12th minute when Ollie Banks limped off after an accidental clash with Jimmy Ryan.
Sam Hird, who came on to replace Banks in midfield, soon went close to making an impact. Jay O'Shea sent over a corner which was met by a far post header from Hird, who was unlucky to see the ball deflect off Nathaniel Knight-Percival for another corner.
The Spireites were enjoying a good spell of possession and Doyle had a shot deflected wide.
After Lee got down bravely to claim the ball at the feet of Joe Newell, Gary Roberts made an appeal for a penalty after going down in the area as he tried to get past Brisley.
Tendayi Darikwa then created a great opening, skipping past McQuoid inside the area before squaring to Sam Morsy, who sliced his shot wide from a good position.
Ian Evatt also threatened to score, heading straight at keeper Bobby Olejnik after meeting a Roberts free-kick with a far post header.
Brisley (38) put Peterborough further ahead when he got in front of Liam Cooper from Danny Swanson's corner and beat Lee with a firm header.
Skipper Evatt left the field with blood pouring from a cut above his left eye and re-appeared with a head bandage.
Just before the break, Roberts played a searching ball into the area which Doyle just failed to meet.
Swanson had the first effort of the second half, putting a curling effort wide from inside the area.
Doyle (53) then reduced the arrears, swivelling on the edge of the six-yard box to fire home following a driving run into the area from Morsy.
Another probing ball from Roberts - a neat chip into the area - nearly set up Doyle again, but the ball evaded the striker's leap.
Ritchie Humphreys conceded a free-kick in a central position around 25 yards out, receiving a yellow card as a result. The free-kick was taken by Grant McCann whose curling effort was saved by Lee down low to his right.
Peterborough were reduced to ten men in the 68th minute when Newell was shown a straight red card after kicking out at Morsy.
Roberts became the second Chesterfield player to receive a booking when he fouled Swanson after tracking back.
Manager Cook made a second substitution when teenager Mason Bennett, on loan from Derby County, replaced Jay O'Shea.
Peterborough restored their two-goal lead when they were awarded a penalty after Cooper was adjudged to have fouled Mark Little inside the area. Assombalonga (77) tucked away the spot-kick, firing straight down the middle.
Marc Richards was sent on a couple of minutes later as Cook made his final substitution, with Hird the one to make way.
Morsy threatened in stoppage time with a goal-bound shot which was blocked and his follow up saved by Olejnik.
Chesterfield: Lee, Darikwa, Evatt, Cooper, Humphreys, O'Shea (Bennett 72), Morsy, Ryan, Banks (Hird 12) (Richards (79), Roberts, Doyle
Peterborough United: Olejnik, Little, Bostwick, Brisley (Alcock 72), Knight-Percival, McCann (Payne 67), Swanson, Rowe, Newell, McQuoid (Isgrove 83), Assombalonga
Goals - Chesterfield: Doyle (53)
Peterborough: McQuoid (7), Brisley (38), Assombalonga pen (77)