Nahki Wells and Ricky Ravenhill had twice put Bradford ahead only for Tendayi Darikwa and Togwell to hit back for the home side, who still harbour outside play-off hopes of their own.
The travelling Bradford fans saw their side survive a scare in the ninth minute as Conor Townsend's inswinging corner was poked goalwards by Drew Talbot but Gary Jones cleared off the line.
Chesterfield had another good chance in the 29th minute when Jay O'Shea put Darikwa in on the right but his shot was well saved by Jon McLaughlin, and the visitors took advantage to go ahead seven minutes later.
A throw-in was flicked on to the unmarked Wells, who turned to hit a left-footed foot shot from 15 yards across Tommy Lee and into the bottom corner for his 22nd goal of the season.
Wells was only denied another to add to his tally by a great block from Liam Cooper early in the second half, but Chesterfield equalised in the 70th minute when Darikwa swept in a cross from the right.
Bradford were back in front in the 79th minute when Ravenhill's low shot flashed through a crowd of players but Togwell levelled once more with a low shot from a corner in the second minute of stoppage time.