Sam Saunders gave the home side an early lead when he fired them ahead with a powerful 20-yard strike in the second minute, before substitute Mark Nwokeji and then striker Paul Benson sealed the points with two late goals.
Chesterfield hit the self-destruct button either side of half time when they went down to nine men after the sending off of Lloyd Kerry and then skipper Robert Page.
The Spireites pushed forward in search of an equaliser with the best chance falling to Kevin Austin, who powered a bullet header against the crossbar in the 20th minute.
Kerry undid his side's hard work in the 37th minute when he saw red after swinging a punch at Ben Strevens.
The Spireites had Trevor Carson to thank for keeping them in the game from the resulting free-kick when he dived bravely to block at the feet of Benson after spilling from Solomon Taiwo.
Chesterfield's day went from bad to worse 11 minutes into the second half when skipper Page was sent off for swinging an elbow during a fierce challenge on Strevens.
Saunders should have made it two for the Daggers in the 68th minute when he slalomed through the Spireites' defence before seeing his close-range shot blocked by Carson.
Carson produced two more superb reflex saves to deny Benson by palming away a point-blank header in the 73rd minute, before blocking at his feet when one on one with the striker five minutes later.
Chesterfield's resistance was finally broken in the 87th minute when Nwokeji came off the bench to power in a thunderous 20 yard strike, with Benson wrapping things up with a poacher's finish from close range a minute later.