Marc Richards put the Spireites in front from the penalty spot after Sam Hird was sent off for the home side but Abu Ogogo equalised with an unstoppable shot in the second half.
Dagenham had goalkeeper Chris Lewington to thank after only four minutes when he turned over an Armand Gnanduillet shot from 12 yards, before he then denied Tendayi Darikwa as Chesterfield dominated.
Yet the visitors should have gone ahead in the 34th minute when Ian Evatt pulled over Zavon Hines in the area, but the striker dragged his penalty yards wide.
Chesterfield were reduced to 10 men three minutes later when Hird tripped Rhys Murphy on the edge of the box.
But Chesterfield were ahead four minutes into the second half when Brian Saah handled a goalbound shot and Richards dispatched the penalty, only for Ogogo to level with a stunning shot from the edge of the area in the 58th minute.
Lewington made another fine save from a Richards header but Dagenham almost won it when Murphy hit a post late on.