Josh Rees put the Daggers ahead in the first-half but after Harry Phipps was sent off with 20 minutes remaining a free-kick from Ryan Colclough, a 90th minute Will Grigg penalty and a finish from Ollie Banks turned the scoreline around.
Coach Danny Webb said: “It was a poor goal for us to concede - a needless free-kick - second phase goal, free shot on goal from five yards so that is not pleasing at all but once again the resilience was great to come back from that.
“I would like to say pride and passion won us the game but I think quality won us the game.
“Yes, they had 10-men and that helped massively, let’s not sweep that under the carpet, but I think there was only one team going to come out of that as winners and that was us.
“Let’s not forget there were a couple of slips in the first-half and we could have been two or three-nil down at half-time while dominating the game.
“Fair play to Dagenham but I think our quality shone through in the end. We ticked a lot of boxes today. The subs that came on helped us get that victory.”
Jeff King was a notable absentee from the matchday squad, with Liam Mandeville filling in admirably at right-back.
On King, Webb said: “He got that hamstring twinge at Aldershot. He was not quite right, but that was not the reason he did not play today. He trained with a little group this morning and his attitude was fantastic.”
And on Mandeville, Webb said: “Liam is one of them who can step up to the plate and play all positions and with him we just felt that with him in that position he would still give us that attacking threat and I think he did that.”
Chesterfield, who remain second in the table, next face Ebbsfleet United away on Saturday.